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RAMANUJAN GRAPH

  • Ramanujan graph
  • Spectral graph theory concept

    spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are

    Ramanujan graph

    Ramanujan_graph

  • Srinivasa Ramanujan
  • Indian mathematician (1887–1920)

    mathematicians Ramanujan graph – Spectral graph theory concept Ramanujan summation – Mathematical techniques for summing divergent infinite series Ramanujan's constant

    Srinivasa Ramanujan

    Srinivasa Ramanujan

    Srinivasa_Ramanujan

  • Expander graph
  • Sparse graph with strong connectivity

    constructions to produce Ramanujan graphs with a fixed vertex size and degree of regularity. The results show the Ramanujan graphs exist for every vertex

    Expander graph

    Expander_graph

  • Ramanujan–Petersson conjecture
  • Unsolved problem in mathematics

    of the Ramanujan conjecture is the explicit construction of Ramanujan graphs by Lubotzky, Phillips and Sarnak. Indeed, the name "Ramanujan graph" was derived

    Ramanujan–Petersson conjecture

    Ramanujan–Petersson_conjecture

  • Glossary of graph theory
  • arrows. radius The radius of a graph is the minimum eccentricity of any vertex. Ramanujan A Ramanujan graph is a graph whose spectral expansion is as

    Glossary of graph theory

    Glossary_of_graph_theory

  • Supersingular isogeny graph
  • Class of expander graphs arising in computational number theory

    to be Ramanujan graphs, graphs with optimal expansion properties for their degree. The proof is based on Pierre Deligne's proof of the Ramanujan–Petersson

    Supersingular isogeny graph

    Supersingular_isogeny_graph

  • Elementary Number Theory, Group Theory and Ramanujan Graphs
  • 2003 mathematics text

    Theory, Group Theory and Ramanujan Graphs is a book in mathematics whose goal is to make the construction of Ramanujan graphs accessible to undergraduate-level

    Elementary Number Theory, Group Theory and Ramanujan Graphs

    Elementary_Number_Theory,_Group_Theory_and_Ramanujan_Graphs

  • Girth (graph theory)
  • Length of a shortest cycle contained in the graph

    finite fields. These remarkable Ramanujan graphs also have large expansion coefficient. The odd girth and even girth of a graph are the lengths of a shortest

    Girth (graph theory)

    Girth_(graph_theory)

  • Brouwer–Haemers graph
  • edges. It is a strongly regular graph, a distance-transitive graph, and a Ramanujan graph. Although its construction is folklore, it was named after Andries

    Brouwer–Haemers graph

    Brouwer–Haemers graph

    Brouwer–Haemers_graph

  • List of things named after Srinivasa Ramanujan
  • theta function Ramanujan graph Ramanujan's tau function Ramanujan's ternary quadratic form Ramanujan prime Ramanujan's constant Ramanujan's lost notebook

    List of things named after Srinivasa Ramanujan

    List_of_things_named_after_Srinivasa_Ramanujan

  • Pseudorandom graph
  • Graph obeys some properties of random graphs

    In graph theory, a graph is said to be a pseudorandom graph if it obeys certain properties that random graphs obey with high probability. There is no concrete

    Pseudorandom graph

    Pseudorandom_graph

  • Alon–Boppana bound
  • Second-largest eigenvalue lower bound

    eigenvector. The graphs that come close to meeting this bound are Ramanujan graphs, which are examples of the best possible expander graphs. Its discoverers

    Alon–Boppana bound

    Alon–Boppana_bound

  • Ihara zeta function
  • reinterpreted graph-theoretically. It was Toshikazu Sunada who put this suggestion into practice in 1985. As observed by Sunada, a regular graph is a Ramanujan graph

    Ihara zeta function

    Ihara_zeta_function

  • Cheeger constant (graph theory)
  • Measure of whether or not a graph has a "bottleneck"

    Miguel A (2006-08-07). "Optimal network topologies: expanders, cages, Ramanujan graphs, entangled networks and all that". Journal of Statistical Mechanics:

    Cheeger constant (graph theory)

    Cheeger constant (graph theory)

    Cheeger_constant_(graph_theory)

  • Adam Marcus (mathematician)
  • American mathematician (born 1979)

    2021 for their solution to long-standing conjectures in the study of Ramanujan graphs. Marcus grew up in Marietta, Georgia and was a boarding student at

    Adam Marcus (mathematician)

    Adam_Marcus_(mathematician)

  • Nikhil Srivastava
  • California, US-based mathematician

    solving long-standing questions on the Kadison-Singer problem and on Ramanujan graphs.[1] In 2022 The Ciprian Foias Prize in Operator Theory was awarded

    Nikhil Srivastava

    Nikhil Srivastava

    Nikhil_Srivastava

  • Cage (graph theory)
  • Regular graph with fewest possible nodes for its girth

    (1988), "Ramanujan graphs", Combinatorica, 8 (3): 261–277, doi:10.1007/BF02126799, MR 0963118. Tutte, W. T. (1947), "A family of cubical graphs", Proc.

    Cage (graph theory)

    Cage (graph theory)

    Cage_(graph_theory)

  • Riemann hypothesis
  • Conjecture on zeros of the zeta function

    the two-by-two p-adic special linear group. A regular finite graph is a Ramanujan graph, a mathematical model of efficient communication networks, if

    Riemann hypothesis

    Riemann hypothesis

    Riemann_hypothesis

  • Zemor's decoding algorithm
  • Coding theory algorithm

    regular bipartite graphs with arbitrarily large number of vertices such that each graph G {\displaystyle G} in the sequence is a Ramanujan graph. It is called

    Zemor's decoding algorithm

    Zemor's_decoding_algorithm

  • Peter Sarnak
  • South African-born mathematician

    (with A. Lubotzky and R. Phillips) applied results in number theory to Ramanujan graphs, with connections to combinatorics and computer science. Sarnak has

    Peter Sarnak

    Peter Sarnak

    Peter_Sarnak

  • Adjacency matrix
  • Square matrix used to represent a graph or network

    2{\sqrt {d-1}}-o(1)} . This bound is tight in the Ramanujan graphs. Suppose two directed or undirected graphs G1 and G2 with adjacency matrices A1 and A2 are

    Adjacency matrix

    Adjacency_matrix

  • Alexander Lubotzky
  • Israeli mathematician and former politician

    research on growth rates in group theory and on the construction of Ramanujan graphs in graph theory. Alexander (Alex) Lubotzky was born in Tel Aviv to Holocaust

    Alexander Lubotzky

    Alexander Lubotzky

    Alexander_Lubotzky

  • Brandt matrix
  •  75–151, ISBN 3-540-06219-X, Zbl 0258.10013 Pizer, Arnold K. (1998), "Ramanujan graphs", in Buell, D.A.; Teitelbaum, J.T. (eds.), Computational perspectives

    Brandt matrix

    Brandt_matrix

  • List of unsolved problems in mathematics
  • combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, mathematical logic, number theory, set theory, Ramsey

    List of unsolved problems in mathematics

    List_of_unsolved_problems_in_mathematics

  • Arithmetic group
  • Type of group in group theory

    can be used to construct expander graphs (Margulis), or even Ramanujan graphs (Lubotzky-Phillips-Sarnak). Such graphs are known to exist in abundance by

    Arithmetic group

    Arithmetic group

    Arithmetic_group

  • Partition function (number theory)
  • Number of partitions of an integer

    Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences

    Partition function (number theory)

    Partition function (number theory)

    Partition_function_(number_theory)

  • Daniel Spielman
  • American computer scientist

    A.; Srivastava, Nikhil (2015), "Interlacing families I: Bipartite Ramanujan graphs of all degrees", Annals of Mathematics, 182 (1): 307–325, arXiv:1304

    Daniel Spielman

    Daniel_Spielman

  • Winnie Li
  • Taiwanese-American mathematician

    theory to construct efficient communication networks called Ramanujan graphs and Ramanujan complexes. Li graduated from National Taiwan University with

    Winnie Li

    Winnie_Li

  • Grigory Margulis
  • Russian mathematician

    gave the first construction of expander graphs, which was later generalized in the theory of Ramanujan graphs. In 1986, Margulis gave a complete resolution

    Grigory Margulis

    Grigory Margulis

    Grigory_Margulis

  • Giuliana Davidoff
  • American mathematician

    Davidoff is a coauthor of: Elementary Number Theory, Group Theory and Ramanujan Graphs (with Peter Sarnak and Alain Valette, 2003) The Geometry of Numbers

    Giuliana Davidoff

    Giuliana_Davidoff

  • Odd cycle transversal
  • In graph theory, an odd cycle transversal of an undirected graph is a set of vertices of the graph that has a nonempty intersection with every odd cycle

    Odd cycle transversal

    Odd cycle transversal

    Odd_cycle_transversal

  • Euclidean algorithm
  • Algorithm for computing greatest common divisors

    of Integer Quaternions". Elementary Number Theory, Group Theory and Ramanujan Graphs. London Mathematical Society Student Texts. Vol. 55. Cambridge University

    Euclidean algorithm

    Euclidean algorithm

    Euclidean_algorithm

  • List of Indian inventions and discoveries
  • Indian inventions

    Kesavan Raghavan Nair in 1939. Ramanujan theta function, Ramanujan prime, Ramanujan summation, Ramanujan graph and Ramanujan's sum – Discovered by the Indian

    List of Indian inventions and discoveries

    List_of_Indian_inventions_and_discoveries

  • 233 (number)
  • Natural number

    Pillai prime, and a Ramanujan prime It is a Fibonacci number, one of the Fibonacci primes There are exactly 233 maximal planar graphs with ten vertices

    233 (number)

    233_(number)

  • Toshikazu Sunada
  • Japanese mathematician (born 1948)

    work, see also Isospectral, Reinhardt domain, Ihara zeta function, Ramanujan graph, quantum ergodicity, quantum walk. T. Sunada, Holomorphic equivalence

    Toshikazu Sunada

    Toshikazu Sunada

    Toshikazu_Sunada

  • Machtey Award
  • Results for Structured Linear Systems" 2016 Michael B. Cohen (MIT) "Ramanujan Graphs in Polynomial Time" Aviad Rubinstein (Berkeley) "Settling the Complexity

    Machtey Award

    Machtey_Award

  • Ramanujan Institute for Advanced Study in Mathematics
  • 13°03′53″N 80°16′48″E / 13.0646°N 80.2801°E / 13.0646; 80.2801 Ramanujan Institute for Advanced Study in Mathematics (RIASM) is the Department of Mathematics

    Ramanujan Institute for Advanced Study in Mathematics

    Ramanujan_Institute_for_Advanced_Study_in_Mathematics

  • Erdős number
  • Degrees of separation from Paul Erdős

    Srinivasa Ramanujan has an Erdős number of only 3 (through G. H. Hardy, Erdős number 2), even though Paul Erdős was only 7 years old when Ramanujan died.

    Erdős number

    Erdős number

    Erdős_number

  • Steiner tree problem
  • On short connecting nets with added points

    term Steiner tree problem, is the Steiner tree problem in graphs. Given an undirected graph with non-negative edge weights and a subset of vertices, usually

    Steiner tree problem

    Steiner tree problem

    Steiner_tree_problem

  • National Mathematics Talent Contest
  • India's national-level mathematics contest conducted by the (AMTI)

    the Bhaskara Contest Inter level: Standards 11 and 12, is called the Ramanujan Contest Senior level: B.Sc. students, is called the Aryabhata Contest

    National Mathematics Talent Contest

    National_Mathematics_Talent_Contest

  • Alexei Venkov
  • Russian mathematician

    1993, pp. 527–538 with A. M. Nikitin: The Selberg trace formula, Ramanujan graphs and some problems in mathematical physics, Saint Petersburg Mathematical

    Alexei Venkov

    Alexei_Venkov

  • Metric dimension (graph theory)
  • Number of vertices with unambiguous distances

    Belmonte, R.; Fomin, F. V.; Golovach, P. A.; Ramanujan, M. S. (2015), "Metric dimension of bounded width graphs", in Italiano, G. F.; Pighizzini, G.; Sannella

    Metric dimension (graph theory)

    Metric_dimension_(graph_theory)

  • Biclique-free graph
  • Property in graph theory

    Daniel; Mouawad, Amer E.; Panolan, Fahad; Ramanujan, M. S.; Saurabh, Saket (2015), "Reconfiguration on sparse graphs", in Dehne, Frank; Sack, Jörg-Rüdiger;

    Biclique-free graph

    Biclique-free_graph

  • Ralph S. Phillips
  • American mathematician

    mathematics at Stanford. Philips's work (with A. Lubotzky and P. Sarnak) on Ramanujan graphs had a huge impact on combinatorics and computer science. Scattering

    Ralph S. Phillips

    Ralph_S._Phillips

  • Stochastic block model
  • Concept in network science

    stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized

    Stochastic block model

    Stochastic block model

    Stochastic_block_model

  • Yasutaka Ihara
  • Japanese mathematician

    by Toshikazu Sunada in 1985. Sunada also proved that a regular graph is a Ramanujan graph if and only if its Ihara zeta function satisfies an analogue of

    Yasutaka Ihara

    Yasutaka_Ihara

  • Expander walk sampling
  • . Such families exist and are efficiently constructible, e.g. the Ramanujan graphs of Lubotzky-Phillips-Sarnak. Doob, J.L. (1953). Stochastic Processes

    Expander walk sampling

    Expander_walk_sampling

  • Integer partition
  • Decomposition of an integer as a sum of positive integers

    } Srinivasa Ramanujan discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences. For

    Integer partition

    Integer partition

    Integer_partition

  • 12 (number)
  • Natural number

    {\displaystyle \Delta (q)} whose Fourier coefficients are given by the Ramanujan τ {\displaystyle \tau } -function and which is (up to a constant multiplier)

    12 (number)

    12_(number)

  • 27 (number)
  • Natural number

    Zbl 1320.51021. Axler, Christian (2023). "On Robin's inequality". The Ramanujan Journal. 61 (3). Heidelberg, GE: Springer: 909–919. arXiv:2110.13478.

    27 (number)

    27_(number)

  • 1728 (number)
  • Natural number

    5} minichess is 1728. 1728 is one less than the first taxicab or Hardy–Ramanujan number 1729, which is the smallest number that can be expressed as sums

    1728 (number)

    1728_(number)

  • Matroid girth
  • Abstraction of graph shortest cycles

    generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, Hall sets in bipartite graphs, even sets in families of sets, and general

    Matroid girth

    Matroid_girth

  • Approximations of pi
  • Varying methods used to calculate pi

    {7}}{\sqrt {11}}}}} This is derived from Ramanujan's class invariant G385. third harmonic of the Ramanujan constant, accurate to 60 decimal places: ln

    Approximations of pi

    Approximations of pi

    Approximations_of_pi

  • List of theorems
  • (combinatorics) Graph structure theorem (graph theory) Grinberg's theorem (graph theory) Grötzsch's theorem (graph theory) Hajnal–Szemerédi theorem (graph theory)

    List of theorems

    List_of_theorems

  • Integral
  • Operation in mathematical calculus

    computes the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally

    Integral

    Integral

    Integral

  • Shai Evra
  • Israeli mathematician

    awarded the SASTRA Ramanujan Prize in 2020. He researches symmetric spaces of arithmetic groups. According to the SASTRA Ramanujan Prize citation, Shai

    Shai Evra

    Shai_Evra

  • List of open-access journals
  • of Mathematics Hardy-Ramanujan Journal Journal de Théorie des Nombres de Bordeaux Journal of Formalized Reasoning Journal of Graph Algorithms and Applications

    List of open-access journals

    List_of_open-access_journals

  • Almost all
  • In mathematics, with negligible exceptions

    p + g. In graph theory, if A is a set of (finite labelled) graphs, it can be said to contain almost all graphs, if the proportion of graphs with n vertices

    Almost all

    Almost_all

  • Outline of combinatorics
  • Overview of and topical guide to combinatorics

    Journal of Analytic Combinatorics Optimization Methods and Software The Ramanujan Journal Séminaire Lotharingien de Combinatoire SIAM Journal on Discrete

    Outline of combinatorics

    Outline_of_combinatorics

  • Stirling's approximation
  • Approximation for factorials

    alternative approximation for the gamma function stated by Srinivasa Ramanujan in Ramanujan's lost notebook is Γ ( 1 + x ) ≈ π ( x e ) x ( 8 x 3 + 4 x 2 + x

    Stirling's approximation

    Stirling's approximation

    Stirling's_approximation

  • Pál Turán
  • Hungarian mathematician

    analysis and graph theory. In 1934, Turán used the Turán sieve to give a new and very simple proof of a 1917 result of G. H. Hardy and Ramanujan on the normal

    Pál Turán

    Pál Turán

    Pál_Turán

  • Fransén–Robinson constant
  • Mathematical constant

    denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1/Γ(x), and the positive x axis. That

    Fransén–Robinson constant

    Fransén–Robinson constant

    Fransén–Robinson_constant

  • Gelfond's constant
  • Constant e raised to the power of pi

    and that the Indian mathematical genius Srinivasa Ramanujan had predicted it—hence its name. Ramanujan's constant is also a transcendental number. The coincidental

    Gelfond's constant

    Gelfond's_constant

  • Pi
  • Number, approximately 3.14

    algorithms were anticipated in 1914, when Indian mathematician Srinivasa Ramanujan published dozens of innovative new formulae for π, remarkable for their

    Pi

    Pi

  • 2000 (number)
  • Natural number

    The OEIS Foundation, Inc. Retrieved 13 November 2012. Ono, Ken (1997). "Ramanujan, taxicabs, birthdates, zipcodes and twists" (PDF). American Mathematical

    2000 (number)

    2000_(number)

  • Logarithmic integral function
  • Special function defined by an integral

    39684 85892 02744 94930... OEIS: A070769; this number is known as the Ramanujan–Soldner constant. li ⁡ ( Li − 1 ( 0 ) ) = li ( 2 ) {\displaystyle \operatorname

    Logarithmic integral function

    Logarithmic integral function

    Logarithmic_integral_function

  • 700 (number)
  • Natural number

    in expressions for Ramanujan's constant and other almost integers. 745 = 5 × 149. There are 745 non-connected simple labeled graphs covering 6 vertices

    700 (number)

    700_(number)

  • Harmonic series (mathematics)
  • Divergent sum of positive unit fractions

    harmonic sums". The Ramanujan Journal. 37: 89–108. doi:10.1007/s11139-014-9600-9. S2CID 254990799. Delabaere, Éric (2003). "Ramanujan's Summation" (PDF)

    Harmonic series (mathematics)

    Harmonic_series_(mathematics)

  • 7
  • Natural number

    and x natural. In particular, the equation 2n − 7 = x2 is known as the Ramanujan–Nagell equation. 7 is one of seven numbers in the positive definite quadratic

    7

    7

  • Undefined (mathematics)
  • Expression which is not assigned an interpretation

    they are both internally consistent and practically useful. For example, Ramanujan summation may seem unintuitive, as it works upon divergent series that

    Undefined (mathematics)

    Undefined_(mathematics)

  • Orders of magnitude (numbers)
  • different ways. It is known as the Ramanujan number or Hardy–Ramanujan number after G. H. Hardy and Srinivasa Ramanujan. Typesetting: 2,000–3,000 letters

    Orders of magnitude (numbers)

    Orders_of_magnitude_(numbers)

  • Catalan's constant
  • Number, approximately 0.916

    foundations for such series are given by Broadhurst, for the first formula, and Ramanujan, for the second formula. The algorithms for fast evaluation of the Catalan

    Catalan's constant

    Catalan's constant

    Catalan's_constant

  • List of mathematics journals
  • Geometry, and Dynamics Hacettepe Journal of Mathematics and Statistics Hardy–Ramanujan Journal Hiroshima Mathematical Journal Historia Mathematica Homology,

    List of mathematics journals

    List_of_mathematics_journals

  • Zero-sum problem
  • Mathematical problem

    "On Kemnitz' conjecture concerning lattice-points in the plane", The Ramanujan Journal, 13 (1–3): 333–337, arXiv:1603.06161, doi:10.1007/s11139-006-0256-y

    Zero-sum problem

    Zero-sum_problem

  • 1000 (number)
  • number, Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number. In the decimal expansion of e the first time all 10 digits appear

    1000 (number)

    1000_(number)

  • Birthday problem
  • Probability of shared birthdays

    +{\frac {(M-1)(M-2)\cdots 1}{M^{M-1}}}} has been studied by Srinivasa Ramanujan and has asymptotic expansion: Q ( M ) ∼ π M 2 − 1 3 + 1 12 π 2 M − 4 135

    Birthday problem

    Birthday problem

    Birthday_problem

  • List of women in mathematics
  • German number theorist, expert on mock theta functions, winner of SASTRA Ramanujan Prize Ruth Britto, American mathematical physicist Jill Britton (1944–2016)

    List of women in mathematics

    List_of_women_in_mathematics

  • Lucy Joan Slater
  • British mathematician (1922-2008)

    hypergeometric functions, and who found many generalizations of the Rogers–Ramanujan identities. Slater was born in 1922 and homeschooled for much of her early

    Lucy Joan Slater

    Lucy_Joan_Slater

  • Greek letters used in mathematics, science, and engineering
  • Symbols for constants, special functions

    correlation coefficient, a measure of rank correlation in statistics Ramanujan's tau function in number theory shear stress in continuum mechanics a type

    Greek letters used in mathematics, science, and engineering

    Greek_letters_used_in_mathematics,_science,_and_engineering

  • Lists of mathematics topics
  • of things named after Pythagoras List of things named after Srinivasa Ramanujan List of things named after Bernhard Riemann List of things named after

    Lists of mathematics topics

    Lists_of_mathematics_topics

  • Floor and ceiling functions
  • Nearest integers from a number

    " Ramanujan, Question 723, Papers p. 332 Somu, Sai Teja; Kukla, Andrzej (2022). "On some generalizations to floor function identities of Ramanujan" (PDF)

    Floor and ceiling functions

    Floor and ceiling functions

    Floor_and_ceiling_functions

  • Euler's totient function
  • Number of integers coprime to and less than n

    theorem Highly composite number Multiplicative group of integers modulo n Ramanujan sum Totient summatory function (𝛷) "Euler's totient function". Khan Academy

    Euler's totient function

    Euler's totient function

    Euler's_totient_function

  • List of long mathematical proofs
  • theorem, which bring to total length up to more than 700 pages. 1974 – Ramanujan conjecture and the Weil conjectures. While Deligne's final paper proving

    List of long mathematical proofs

    List_of_long_mathematical_proofs

  • Theta function (disambiguation)
  • Topics referred to by the same term

    \phi (q),\psi (q),\chi (q)} , etc., a mock modular form of weight 1/2 Ramanujan theta function, f ( a , b ) {\displaystyle f(a,b)} Neville theta functions

    Theta function (disambiguation)

    Theta_function_(disambiguation)

  • Gamma function
  • Extension of the factorial function

    evaluation by contour integration methods and some related results". Ramanujan J. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. S2CID 120943474. Blagouchine

    Gamma function

    Gamma function

    Gamma_function

  • Analytic Combinatorics (book)
  • 2009 book on combinatorial enumeration

    combinatorics goes back at least to the work of G. H. Hardy and Srinivasa Ramanujan on the partition function, the citation also quoted a review by Robin

    Analytic Combinatorics (book)

    Analytic_Combinatorics_(book)

  • Exponential integral
  • Special function defined by an integral

    inaccurate due to cancellation. A faster converging series was found by Ramanujan: E i ( x ) = γ + ln ⁡ x + exp ⁡ ( x / 2 ) ∑ n = 1 ∞ ( − 1 ) n − 1 x n

    Exponential integral

    Exponential integral

    Exponential_integral

  • Modular lambda function
  • Symmetric holomorphic function

    ^{*}(169x)}{1-\lambda ^{*}(169x)^{2}}}\right]^{1/12}\right)\end{aligned}}} Ramanujan's class invariants G n {\displaystyle G_{n}} and g n {\displaystyle g_{n}}

    Modular lambda function

    Modular lambda function

    Modular_lambda_function

  • List of conjectures
  • Hirsch conjecture (disproved 2010) Kaplansky unit conjecture Intersection graph conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture

    List of conjectures

    List_of_conjectures

  • List of probabilistic proofs of non-probabilistic theorems
  • numbers (see also the first item of the section Analysis). The Rogers–Ramanujan identities are proved using Markov chains. A non-probabilistic proof was

    List of probabilistic proofs of non-probabilistic theorems

    List_of_probabilistic_proofs_of_non-probabilistic_theorems

  • Navin M. Singhi
  • Indian mathematician (born 1949)

    Institute of Fundamental Research, Mumbai, specializing in combinatorics and graph theory. He is the recipient of the prestigious Shanti Swarup Bhatnagar Prize

    Navin M. Singhi

    Navin_M._Singhi

  • Ben Green (mathematician)
  • British mathematician (born 1977)

    Clay Research Award 2005: Salem Prize 2005: Whitehead Prize 2007: SASTRA Ramanujan Prize 2008: European Mathematical Society prize recipient 2014: Sylvester

    Ben Green (mathematician)

    Ben Green (mathematician)

    Ben_Green_(mathematician)

  • Monte Carlo tree search
  • Heuristic search algorithm for evaluating game trees

    pp. 258–269. doi:10.1007/978-3-642-31866-5_22. ISBN 978-3-642-31865-8. Ramanujan, Raghuram; Sabharwal, Ashish; Selman, Bart (May 2010). "On adversarial

    Monte Carlo tree search

    Monte_Carlo_tree_search

  • Computational complexity of mathematical operations
  • Algorithmic runtime requirements for common math procedures

    (1988). "Approximations and complex multiplication according to Ramanujan". Ramanujan revisited: Proceedings of the Centenary Conference. Academic Press

    Computational complexity of mathematical operations

    Computational complexity of mathematical operations

    Computational_complexity_of_mathematical_operations

  • History of mathematics
  • Revisited". The Legacy of Srinivasa Ramanujan, RMS-Lecture Notes Series. 20: 261–279. Bradley, David M. (2005-05-07), Ramanujan's formula for the logarithmic

    History of mathematics

    History of mathematics

    History_of_mathematics

  • Nørlund–Rice integral
  • Mathematical integral

    of finite differences and has also been applied in computer science and graph theory to estimate binary tree lengths. It is named in honour of Niels Erik

    Nørlund–Rice integral

    Nørlund–Rice_integral

  • WARFT
  • Nanotech DSP Architectures Group NAREN: Testing and Fault Tolerant Group RAMANUJAN: Nanotech Design Methodologies Group HARDY: Low Power Architectures for

    WARFT

    WARFT

  • Pythagorean prime
  • Prime number congruent to 1 mod 4

    a Paley graph with p {\displaystyle p} vertices, representing the numbers modulo p {\displaystyle p} , with two numbers adjacent in the graph if and only

    Pythagorean prime

    Pythagorean prime

    Pythagorean_prime

  • Erdős distinct distances problem
  • Problem in discrete geometry

    which are sums of two squares, expressed in big O notation; see Landau–Ramanujan constant. Erdős conjectured that the upper bound O ( n / log ⁡ n ) {\displaystyle

    Erdős distinct distances problem

    Erdős_distinct_distances_problem

  • Prime-counting function
  • Function representing the number of primes less than or equal to a given number

    (}\pi _{0}(x)-\operatorname {R} (x){\bigr )}{\frac {\log x}{\sqrt {x}}}.} Ramanujan proved that the inequality π ( x ) 2 < e x log ⁡ x π ( x e ) {\displaystyle

    Prime-counting function

    Prime-counting function

    Prime-counting_function

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Online names & meanings

  • Ida
  • Surname or Lastname

    English and German

    Ida

    English and German : from Ida, which is found as both a male and female personal name in English but only as a female name in German. This is of continental Germanic origin and was popular among the Normans, who brought it to England. Its etymology is disputed: it is thought by some to be of the same origin as hild- ‘battle’, ‘strife’; by others to be of the same origin as Old High German idis ‘(wise) woman’, or from Old Norse idh ‘work’, ‘activity’.Japanese : ‘rice paddy by the well’; habitational name from Ida-mura in Musashi (now Tōkyō and Saitama prefectures). Variously written and found mostly in eastern Japan and the Ryūkyū Islands.

  • Melana
  • Girl/Female

    Latin

    Melana

    Dark.

  • Darnel
  • Boy/Male

    English

    Darnel

    Hiding place; hidden area.

  • Barsin
  • Girl/Female

    Indian, Parsi

    Barsin

    Clover; Brilliant

  • Ib
  • Boy/Male

    Phoenician

    Ib

    Oath of Baol.

  • Brenn
  • Girl/Female

    British, English, Gaelic, Irish, Norse

    Brenn

    Burning; Raven; Black Haired; Stinking Hair; Sword

  • Kerrin
  • Girl/Female

    Hebrew

    Kerrin

    Beauty. Abbreviation of Kerenhappuch.

  • Fairleigh
  • Surname or Lastname

    English

    Fairleigh

    English : possibly a variant of Scottish Fairley.

  • Pankanabh
  • Boy/Male

    Hindu, Indian, Traditional

    Pankanabh

    Lotus Flower

  • Prathysha
  • Girl/Female

    Hindu

    Prathysha

    Saisudha, Early morning, Dawn

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Other words and meanings similar to

RAMANUJAN GRAPH

AI search in online dictionary sources & meanings containing RAMANUJAN GRAPH

RAMANUJAN GRAPH

  • Graphical
  • a.

    Having the faculty of, or characterized by, clear and impressive description; vivid; as, a graphic writer.

  • Thermometrograph
  • n.

    An instrument for recording graphically the variations of temperature, or the indications of a thermometer.

  • Stylus
  • n.

    A pen-shaped pointing device used to specify the cursor position on a graphics tablet.

  • Rational
  • a.

    Expressing the type, structure, relations, and reactions of a compound; graphic; -- said of formulae. See under Formula.

  • Graphitoid
  • a.

    Alt. of Graphitoidal

  • Plumbago
  • n.

    Same as Graphite.

  • Graphic
  • a.

    Alt. of Graphical

  • Graphicalness
  • n.

    The quality or state of being graphic.

  • Graphitoidal
  • a.

    Resembling graphite or plumbago.

  • Graphitic
  • a.

    Pertaining to, containing, derived from, or resembling, graphite.

  • Hyetograph
  • n.

    A chart or graphic representation of the average distribution of rain over the surface of the earth.

  • Graphically
  • adv.

    In a graphic manner; vividly.

  • Sphygmograph
  • n.

    An instrument which, when applied over an artery, indicates graphically the movements or character of the pulse. See Sphygmogram.

  • Graphicness
  • n.

    Alt. of Graphicalness

  • Sylvanite
  • n.

    A mineral, a telluride of gold and silver, of a steel-gray, silver-white, or brass-yellow color. It often occurs in implanted crystals resembling written characters, and hence is called graphic tellurium.

  • Map
  • n.

    Anything which represents graphically a succession of events, states, or acts; as, an historical map.

  • Portrait
  • n.

    Hence, any graphic or vivid delineation or description of a person; as, a portrait in words.

  • Graphiscope
  • n.

    See Graphoscope.

  • Pot
  • n.

    A crucible; as, a graphite pot; a melting pot.

  • Kymograph
  • n.

    An instrument for measuring, and recording graphically, the pressure of the blood in any of the blood vessels of a living animal; -- called also kymographion.