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Generalization of the concept from statistical mechanics
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition
Partition function (mathematics)
Partition_function_(mathematics)
Function in thermodynamics and statistical physics
of partition functions can be defined for different circumstances; see partition function (mathematics) for generalizations. The partition function has
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Topics referred to by the same term
of a molecule Partition function (quantum field theory), partition function for quantum path integrals Partition function (mathematics), generalization
Partition_function
Physical function in thermodynamics
statistical mechanics, the translational partition function, q T {\displaystyle q_{T}} is that part of the partition function resulting from the movement (translation)
Translational partition function
Translational_partition_function
Function in Chemistry
rotational partition function relates the rotational degrees of freedom to the rotational part of the energy. The total canonical partition function Z {\displaystyle
Rotational_partition_function
Decomposition of an integer as a sum of positive integers
same partition as 2 + 1 + 1. An individual summand in a partition is called a part. The number of partitions of n is given by the partition function p(n)
Integer_partition
Number of partitions of an integer
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because
Partition function (number theory)
Partition_function_(number_theory)
The vibrational partition function traditionally refers to the component of the canonical partition function resulting from the vibrational degrees of
Vibrational partition function
Vibrational_partition_function
Expectation value of time-ordered quantum operators
treated separately. Effective action Green's function (many-body theory) Partition function (mathematics) Source field The − i {\displaystyle -i} factor
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
In representation theory, a branch of mathematics, the Kostant partition function, introduced by Bertram Kostant (1958, 1959), of a root system Δ {\displaystyle
Kostant_partition_function
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are partition of a set
List_of_partition_topics
Set of functions from a topological space to [0,1] which sum to 1 for any input
In mathematics, a partition of unity on a topological space X {\displaystyle X} is a set R {\displaystyle R} of continuous functions from X
Partition_of_unity
Topics referred to by the same term
of unity, of a topological space Plane partition, in mathematics and especially combinatorics Graph partition, the reduction of a graph to a smaller graph
Partition
Some remarkable congruences for the partition function
In mathematics, Ramanujan's congruences are the congruences for the partition function p(n) discovered by Srinivasa Ramanujan: p ( 5 k + 4 ) ≡ 0 ( mod
Ramanujan's_congruences
Mathematical ways to group elements of a set
In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one
Partition_of_a_set
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some
List of mathematical functions
List_of_mathematical_functions
Physics of many interacting particles
variance Negative probability Gibbs state Master equation Partition function (mathematics) Quantum probability Percolation theory Schramm–Loewner evolution
Statistical_mechanics
Function defined by multiple sub-functions
In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose
Piecewise_function
Mathematical function such that every output has at least one input
In mathematics, a surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's
Surjective_function
Mathematical ranking of a set
utility function is also possible. Weak orderings are counted by the ordered Bell numbers. They are used in computer science as part of partition refinement
Weak_ordering
published in 1918 stated and proved the following congruences for the partition function p(n), since known as Ramanujan congruences. p(5n + 4) ≡ 0 (mod 5)
Crank_of_a_partition
Mathematical concept for comparing objects
transformation group (and an automorphism group) because function composition preserves the partitioning of A . ◼ {\displaystyle A.\blacksquare } Wallace, D
Equivalence_relation
Symmetric function invariant of graphs
function is a symmetric function invariant of graphs studied in algebraic graph theory, a branch of mathematics. It is the weight generating function
Chromatic_symmetric_function
Study of discrete mathematical structures
continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes
Discrete_mathematics
On integer partitions from monotonic functions
theorem is a mathematical description of the partitions of natural numbers into two complementary sets. For instance, it applies to the partition of numbers
Lambek–Moser_theorem
Operation in mathematical calculus
such a tagged partition is the width of the largest sub-interval formed by the partition, maxi=1...n Δi. The Riemann integral of a function f over the interval
Integral
Method of mathematical integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that
Lebesgue_integral
Array of nonnegative integers in combinatorics
In mathematics and especially in combinatorics, a plane partition is a two-dimensional array of nonnegative integers π i , j {\displaystyle \pi _{i,j}}
Plane_partition
Count of the possible partitions of a set
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th
Bell_number
Basic integral in elementary calculus
suitable functions, including every continuous function on a closed bounded interval, these Riemann sums approach a single limiting value as the partitions of
Riemann_integral
Set of all points in a function's domain that all map to some single given point
In mathematics, the fiber (US English) or fibre (British English) of an element y {\displaystyle y} under a function f {\displaystyle f} is the preimage
Fiber_(mathematics)
Property of mathematical objects
In mathematics, a rigid collection C of mathematical objects c (for instance sets or functions) is one in which every c ∈ C is uniquely determined by
Rigidity_(mathematics)
Term in number theory and combinatorics
study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept
Rank_of_a_partition
Special functions of several complex variables
In mathematics, theta functions are special functions of several complex variables. Fundamentally, they are a family of continuous functions which encode
Theta_function
2.71828...; base of natural logarithms
number e is a mathematical constant, approximately equal to 2.71828, that is the base of the natural logarithm and exponential function. It is sometimes
E_(mathematical_constant)
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
Collection of mathematical objects
points in space, lines, other geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a
Set_(mathematics)
Axiom of set theory
constructive mathematics avoid the axiom of choice, others embrace it. A choice function (also called selector or selection) is a function f {\displaystyle
Axiom_of_choice
Rational mathematical function indexed by integer partitions
In mathematics, Weingarten functions are rational functions indexed by partitions of integers that can be used to calculate integrals of products of matrix
Weingarten_function
Set of all things that may be the input of a mathematical function
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ( f ) {\displaystyle \operatorname
Domain_of_a_function
Unsolved problem in mathematics
Unsolved problem in mathematics Given arbitrary m, r, are there infinitely many values of n such that the partition function at n is congruent to r mod
Newman's_conjecture
Summability method in physics
In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent
Zeta_function_regularization
Generating function in integrable systems
Tau functions are an important ingredient in the modern mathematical theory of integrable systems, and have numerous applications in a variety of other
Tau function (integrable systems)
Tau_function_(integrable_systems)
Numbers parameterizing ways to partition a set
In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Symbol representing a mathematical object
had a big influence on mathematics ever since. Originally, the term variable was used primarily for the argument of a function, in which case its value
Variable_(mathematics)
Indian mathematician (1887–1920)
such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired
Srinivasa_Ramanujan
Theorem for proving more complex theorems
In mathematics and other fields, a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement.
Lemma_(mathematics)
Degree of differentiability of a function or map
In mathematical analysis, the smoothness describes the number of times a function can be differentiated without producing discontinuities. The smoothness
Smoothness
Probability distribution that has the most entropy of a class
of statistical mixtures. Exponential family Gibbs measure Partition function (mathematics) Maximal entropy random walk - maximizing entropy rate for
Maximum entropy probability distribution
Maximum_entropy_probability_distribution
Mathematical identities related to integer partitions
In mathematics, the Rogers–Ramanujan identities are two identities related to basic hypergeometric series and integer partitions. The identities were
Rogers–Ramanujan_identities
Basic notion of sameness in mathematics
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical
Equality_(mathematics)
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
One-to-one correspondence
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the
Bijection
Mathematical function
In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane
Dedekind_eta_function
molecular conformations in the partition function. In this sense, the symmetry number depends upon how the partition function is formulated. For example,
Symmetry_number
Mathematical function
In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric
Landau's_function
Branch of mathematics
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis. Originally called
Calculus
All numbers between two given numbers
In mathematics, an interval is the set of all real numbers lying between two fixed endpoints with no "gaps". For example, the set of real numbers consisting
Interval_(mathematics)
Sets with no element in common
In set theory in mathematics and formal logic, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets
Disjoint_sets
On partitions into intersecting convex hulls
Mathematical Notes, 59 (3): 324–326, doi:10.1007/BF02308547, ISSN 1573-8876, S2CID 122078369 Sarkaria, K. S. (November 2000), "Tverberg partitions and
Tverberg's_theorem
Generalization of the Jack polynomial
In mathematics, the Jack function is a generalization of the Jack polynomial, introduced by Henry Jack. The Jack polynomial is a homogeneous, symmetric
Jack_function
Input to a mathematical function
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example
Argument_of_a_function
Mathematical concept
In mathematics, when the elements of some set S {\displaystyle S} have a notion of equivalence (formalized as an equivalence relation), then one may naturally
Equivalence_class
Mathematical function
In mathematics, the Euler function is given by ϕ ( q ) = ∏ k = 1 ∞ ( 1 − q k ) , | q | < 1. {\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k}),\quad
Euler_function
Target set of a mathematical function
In mathematics, a codomain or set of destination of a function is a set into which all of the outputs of the function are constrained to fall. It is the
Codomain
Inputs for which a function's value is non-zero
In mathematics, the support of a real-valued function f {\displaystyle f} is the subset of the function's domain consisting of those elements that are
Support_(mathematics)
Basic framework of mathematics
17th century. This new area of mathematics involved new methods of reasoning and new basic concepts (continuous functions, derivatives, limits) that were
Foundations_of_mathematics
Branch of mathematical logic
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining
Reverse_mathematics
1 and ratio 1/2 Integer partition Irrational number irrationality of log23 irrationality of the square root of 2 Mathematical induction sum identity Power
List_of_mathematical_proofs
In mathematics, solid partitions are natural generalizations of integer partitions and plane partitions defined by Percy Alexander MacMahon. A solid partition
Solid_partition
formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex;
Mathematical_object
Divide and conquer sorting algorithm
gets swapped with other elements in the partition function. Therefore, the index returned in the partition function isn't necessarily where the actual pivot
Quicksort
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Number property of being positive or negative
In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered
Sign_(mathematics)
Subdivision of vertices into disjoint sets
In mathematics, a graph partition is the reduction of a graph to a smaller graph by partitioning its set of nodes into mutually exclusive groups. Edges
Graph_partition
Number of arguments required by a function
In logic, mathematics, and computer science, arity (/ˈærɪti/ ) is the number of arguments or operands taken by a function, operation or relation. In mathematics
Arity
Type of mathematical function
In mathematics, a piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments
Piecewise_linear_function
Branch of mathematics that studies sets
equivalence relations, partitions of sets, and homomorphisms. Thus, many of the usual set-theoretic procedures of twentieth-century mathematics go back to his
Set_theory
Form of mathematical proof
Mathematical induction is a method for proving that a statement P ( n ) {\displaystyle P(n)} is true for every natural number n {\displaystyle n} , that
Mathematical_induction
Function returning one of only two values
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1
Boolean_function
Mathematical formula
For instance, hook partition Schur functions can be expressed bilinearly in terms of elementary and complete symmetric functions, and Schubert classes
Giambelli's_formula
Multiplicative function in number theory
the partition function is the Riemann zeta function. This idea underlies Alain Connes's attempted proof of the Riemann hypothesis. The Möbius function is
Möbius_function
Logical connective AND
In logic, mathematics and linguistics, and ( ∧ {\displaystyle \wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical
Logical_conjunction
Largest and smallest value taken by a function at a given point
In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically
Maximum_and_minimum
Formal power series
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions
Generating_function
Process of repeating items in a self-similar way
logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition
Recursion
Measure of local oscillation behavior
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function
Total_variation
Conjecture in algebraic geometry
curves, and the partition function for the other is the logarithm of the τ-function of the KdV hierarchy. Identifying these partition functions gives Witten's
Witten_conjecture
Mathematical-logic system based on functions
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Branch of discrete mathematics
formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae. Partition theory studies various
Combinatorics
mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss said, "Mathematics
Lists_of_mathematics_topics
Symbolic description of a mathematical object
In mathematics, an expression is an arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can
Expression_(mathematics)
Collection of sets in mathematics that can be defined based on a property of its members
In set theory and its applications throughout mathematics, a class is a collection of mathematical objects (often sets) that can be unambiguously defined
Class_(set_theory)
Theorem in number theory
In mathematics, Euler's pentagonal number theorem relates the product and series representations of the Euler function. It states that ∏ n = 1 ∞ ( 1 −
Pentagonal_number_theorem
Subfield of mathematics
definitions of addition and multiplication from the successor function and mathematical induction. In the mid-19th century, flaws in Euclid's axioms for
Mathematical_logic
Function computable with bounded loops
lies in the fact that most computable functions that are studied in number theory (and more generally in mathematics) are primitive recursive. For example
Primitive_recursive_function
Study of computable functions and Turing degrees
branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing
Computability_theory
Property of operations
k^{n-k}} is the number of different idempotent functions. Hence, taking into account all possible partitions, ∑ k = 0 n ( n k ) k n − k {\displaystyle \sum
Idempotence
Infinite cardinal number
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets.
Aleph_number
Mathematical technique
mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It was introduced in
Transfer-matrix method (statistical mechanics)
Transfer-matrix_method_(statistical_mechanics)
PARTITION FUNCTION-MATHEMATICS
PARTITION FUNCTION-MATHEMATICS
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Biblical
perdition, destruction
Surname or Lastname
English
English : topographic name for someone who lived by a watercourse or road junction, Old English gelǣt, or a habitational name from Leat in Devon, or The Leete in Essex, named with this element.
Girl/Female
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim, Punjabi, Sikh
Wish; Petition to God; Special Prayer
Boy/Male
French Greek
Cyrano de Bergerac was a seventeenth-century soldier and science-fiction writer.
Boy/Male
Hindu, Indian, Traditional
Noble Partition
Girl/Female
Biblical Greek Latin
Perdition, destruction.
Girl/Female
Afghan, Arabic, Australian, Indian, Muslim
Fiction; Romance; Story
Boy/Male
Biblical
That hears, or obeys, perdition.
Girl/Female
Indian
It’s derived from the root word - anksh that means a fraction. Ankshika means the fraction of the cosmos
Girl/Female
Tamil
Ankshika | அஂகà¯à®·à¯€à®•à®¾
It’s derived from the root word - anksh that means a fraction. Ankshika means the fraction of the cosmos
Ankshika | அஂகà¯à®·à¯€à®•à®¾
Girl/Female
Hindu, Indian
Fraction of the Cosmos
Male
English
Hebrew name SHELAH means "a petition, prayer." In the bible, this is the name of a son of Judah. Compare with another form of Shelah.
Biblical
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Boy/Male
Indian
Friction
Boy/Male
Biblical
That hears, or obeys, perdition.
Girl/Female
Bengali, Indian
Fraction of Time
Boy/Male
Indian, Sikh
A Partition in the World
Boy/Male
Arabic
Partition; Curtain
Biblical
Shimeath, that hears, or obeys; perdition
PARTITION FUNCTION-MATHEMATICS
PARTITION FUNCTION-MATHEMATICS
Surname or Lastname
English
English : from the Middle English personal name Elfegh, Alfeg, Old English Ælfhēah, composed of the elements ælf ‘elf’ + hēah ‘high’. The name was sometimes bestowed in honor of St. Alphege (954–1012), archbishop of Canterbury, who was stoned to death by the Danes, and came to be revered as a martyr.
Boy/Male
Indian
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Vishnu
Boy/Male
Hindu, Indian
Light
Boy/Male
Tamil
Unique, Focused
Boy/Male
British, English, Welsh
Affection; Amiable
Surname or Lastname
English
English : patronymic from the personal name Dodde (see Dodd).
Boy/Male
Welsh
Evan's son.
Female
Hebrew
(בֵּית-×ֵל) Hebrew name BEYTH-EL means "house of God." In the bible, this is the name of an ancient city of the Canaanites, later of the Benjamites.Â
Girl/Female
Arabic, Australian, French
Sweet; Cute
PARTITION FUNCTION-MATHEMATICS
PARTITION FUNCTION-MATHEMATICS
PARTITION FUNCTION-MATHEMATICS
PARTITION FUNCTION-MATHEMATICS
PARTITION FUNCTION-MATHEMATICS
v. t.
To sell by auction.
n.
The act of anointing, smearing, or rubbing with an unguent, oil, or ointment, especially for medical purposes, or as a symbol of consecration; as, mercurial unction.
a.
Divided by partition or partitions; having septa; as, a septate pod or shell.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
a.
Denoting a part; as, a partitive genitive.
v. t.
The act of uniting, or the state of being united; junction.
v. t.
To divide into parts or shares; to divide and distribute; as, to partition an estate among various heirs.
n.
A word expressing partition, or denoting a part.
v.
That which divides or separates; that by which different things, or distinct parts of the same thing, are separated; separating boundary; dividing line or space; specifically, an interior wall dividing one part or apartment of a house, an inclosure, or the like, from another; as, a brick partition; lath and plaster partitions.
v. i.
To make a petition or solicitation.
n.
The place or point of union, meeting, or junction; specifically, the place where two or more lines of railway meet or cross.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
a.
Pertaining to the function of an organ or part, or to the functions in general.
v.
The act of parting or dividing; the state of being parted; separation; division; distribution; as, the partition of a kingdom.
n.
The act of joining, or the state of being joined; union; combination; coalition; as, the junction of two armies or detachments; the junction of paths.
imp. & p. p.
of Partition
v. t.
To give sanction to; to ratify; to confirm; to approve.
a.
Pertaining to, or connected with, a function or duty; official.
n.
The things sold by auction or put up to auction.
v. t.
To divide into distinct parts by lines, walls, etc.; as, to partition a house.