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Sequence of integers
mathematics, the Golomb sequence, named after Solomon W. Golomb (but also called Silverman's sequence), is a monotonically increasing integer sequence where an
Golomb_sequence
American mathematician (1932–2016)
tenure two years later. Golomb pioneered the identification of the characteristics and merits of maximum length shift register sequences, also known as pseudorandom
Solomon_W._Golomb
Lossless data compression method
Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s. Alphabets following
Golomb_coding
Ordered list of whole numbers
numbers Golomb sequence Happy numbers Highly composite numbers Highly totient numbers Home primes Hyperperfect numbers Juggler sequence Kolakoski sequence Lucky
Integer_sequence
is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to OEIS
List_of_integer_sequences
Set of marks along a ruler such that no two pairs of marks are the same distance apart
In mathematics, a Golomb ruler is a set of marks at integer positions along a ruler such that no two pairs of marks are the same distance apart. The number
Golomb_ruler
Mathematical constant
In mathematics, the Golomb–Dickman constant, named after Solomon W. Golomb and Karl Dickman, is a mathematical constant, which arises in the theory of
Golomb–Dickman_constant
Infinite sequence in mathematics
Golomb sequence — another self-generating sequence based on run-length Gijswijt's sequence Look-and-say sequence Sloane, N. J. A. (ed.). "Sequence A000002
Kolakoski_sequence
Class of sequences of natural numbers
Therefore all Sidon sets must be Golomb rulers. By a similar argument, all Golomb rulers must be Sidon sets. Moser–de Bruijn sequence Sumset Erdős, P.; Turán,
Sidon_sequence
Type of pseudorandom binary sequence
by Solomon Golomb. The occurrence of 0 and 1 in the sequence should be approximately the same. More precisely, in a maximum-length sequence of length 2
Maximum-length_sequence
Doubly exponential integer sequence
exercise 4.37, p. 147; see also Golomb (1963). Graham, Knuth & Patashnik (1989), p. 109. Sloane, N. J. A. (ed.). "Sequence A000215 (Fermat numbers)". The
Sylvester's_sequence
Number, sum of distinct powers of 4
-1/3} , respectively. Golomb (1966) investigated a subtraction game, analogous to subtract a square, based on this sequence. In Golomb's game, two players
Moser–de_Bruijn_sequence
Points with distinct displacement vectors
arrays can be regarded as two-dimensional cousins of the one-dimensional Golomb ruler construction, and, as well as being of mathematical interest, have
Costas_array
Formula whose values are the prime numbers
Eratosthenes through the Chinese remainder theorem. Inspired by Gandhi's proof, Golomb proved the following recurrence p n = lim s → ∞ ( ζ ( s ) ∏ k = 1 n − 1
Formula_for_primes
Abstract ruler in which some of the distance marks may be missing
of a Golomb ruler. A long Golomb ruler will have gaps, that is, it will have distances which it cannot measure. For example, the optimal Golomb ruler
Sparse_ruler
Natural number
Granville number, or S {\displaystyle {\mathcal {S}}} -perfect number. A Golomb ruler of length 6 is a "perfect ruler". The six exponentials theorem guarantees
6
Numbers whose prime factors all divide the number more than once
integers. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers powerful. Powerful numbers are also known as squarefull
Powerful_number
to arithmetic encoding Entropy coding with known entropy characteristics Golomb coding: form of entropy coding that is optimal for alphabets following geometric
List_of_algorithms
Geometric shape formed from squares
of "dissection problems." The name polyomino was invented by Solomon W. Golomb in 1953, and it was popularized by Martin Gardner in a November 1960 "Mathematical
Polyomino
are the Furstenberg topology on Z {\displaystyle \mathbb {Z} } , and the Golomb topology and the Kirch topology on Z > 0 {\displaystyle \mathbb {Z} _{>0}}
Arithmetic progression topologies
Arithmetic_progression_topologies
Positive integer of the form (2^(2^n))+1
the reciprocals of all the Fermat numbers (sequence A051158 in the OEIS) is irrational. (Solomon W. Golomb, 1963) Fermat numbers and Fermat primes were
Fermat_number
hdl:10831/83020. S2CID 246024152. Weisstein, Eric W. "Perfect Power". MathWorld. Golomb, S.W. (1970). "Powerful numbers". American Mathematical Monthly. 77 (8):
List_of_sums_of_reciprocals
Methods of compressing data tailored specifically for genomic data
to provide additional compression gains. Encoding designs, such as the Golomb code and the Huffman code, have been incorporated into genomic data compression
Compression of genomic sequencing data
Compression_of_genomic_sequencing_data
DNA sequence
molecular biology, the TATA box (also called the Goldberg–Hogness box) is a sequence of DNA found in the core promoter region of genes in archaea and eukaryotes
TATA_box
Type of shift register in computing
1007/978-1-4471-5079-4_2. ISBN 978-1-4471-5079-4. Golomb, Solomon W. (1967). Shift register sequences. Laguna Hills, Calif.: Aegean Park Press. ISBN 978-0-89412-048-0
Linear-feedback shift register
Linear-feedback_shift_register
Chinese-Canadian electrical engineer
The Wisdom Of Solomon: The Genius And Legacy Of Solomon Golomb (edited with Beatrice Golomb and Alfred W. Hales, World Scientific, 2023) Gong was elected
Guang_Gong
String that is strictly smaller in lexicographic order than all of its rotations
between it and Lyndon words was observed by Fredricksen & Maiorana (1978). Golomb (1969). Radford (1979) Berstel, Jean; Perrin, Dominique (2007), "The origins
Lyndon_word
Base-1 numeral system
unary numbering is used as part of some data compression algorithms such as Golomb coding. It also forms the basis for the Peano axioms for formalizing arithmetic
Unary_numeral_system
Abstract strategy game
pile of tokens in two Golomb (1966). Berlekamp, Conway & Guy (2001), "Subtraction games", pp. 83–86. Bouton (1901–1902); Golomb (1966); Berlekamp, Conway
Subtraction_game
Form of lossless data compression
encoding format than long runs. Kolakoski sequence Look-and-say sequence Comparison of graphics file formats Golomb coding Burrows–Wheeler transform Recursive
Run-length_encoding
Weisstein, Eric W. "Thue-Morse Constant". MathWorld. Weisstein, Eric W. "Golomb–Dickman Constant". MathWorld. Weisstein, Eric W. "Lebesgue Constants". MathWorld
List of mathematical constants
List_of_mathematical_constants
Mathematical problem
10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, ... (sequence A005670 in the OEIS) In 1975, Solomon Golomb raised the question whether the whole plane can
Squaring_the_square
Mathematical puzzle
1956, the conjecture was proven by John Selfridge. In 1970, Solomon W. Golomb and John Selfridge showed that the unicursal polygonal path of 2n − 2 segments
Nine_dots_puzzle
Square of a triangular number
Combinatorics, 11 (1), Research Paper 9, doi:10.37236/1762, MR 2034423. Golomb, Solomon W. (1965), "A Geometric Proof of a Famous Identity", The Mathematical
Squared_triangular_number
Type of prefix code
delta coding * ‡ Elias omega coding *[further explanation needed] ‡ Exp-Golomb coding *, which has Elias gamma coding as a special case. (Used in H.264/MPEG-4
Universal code (data compression)
Universal_code_(data_compression)
2017 ballet by Crystal Pite
461–462. Golomb 2023, p. 309. Golomb 2023, pp. 301, 304. Abdo, Attia & Amin 2023, p. 83. Abdo, Attia & Amin 2023, p. 82. Golomb 2023, p. 310. Golomb 2023
Flight_Pattern
Subtraction game
the square numbers. For instance, Golomb defined an analogous game based on the Moser–de Bruijn sequence, a sequence that grows at a similar asymptotic
Subtract_a_square
Numbers whose differences are not squares
invented by Richard A. Epstein and first described in 1966 by Solomon W. Golomb. In this game, two players take turns removing coins from a pile of coins;
Square-difference-free_set
Set of codewords, none a prefix of another
coding Elias omega coding Fibonacci coding Levenshtein coding Unary coding Golomb Rice code Straddling checkerboard (simple cryptography technique which produces
Prefix_code
Encoding which maps information to a variable number of bits
as much as possible so that the source can be recovered with zero error. Golomb code Kruskal count Instruction set architecture § Instruction length in
Variable-length_encoding
Shape with three equal sides
484–485. Grünbaum & Shepard (1977). Grünbaum & Shephard (1987), p. 42. Golomb (1970), p. 10. Niţică (2003), pp. 205–217. Godrèche (1989). Trigg (1978)
Equilateral_triangle
Division of the Semitic languages of the Levant
Semitic and Egyptian Studies Presented to Thomas O. Lambdin. Ed. D. M. Golomb. Winona Lake, IN: Eisenbrauns. pp. 119–39. Harris, Z. 1939. Development
Northwest_Semitic_languages
Form of entropy encoding used in data compression
this purpose. An alternative is encoding run lengths via Huffman-based Golomb-Rice codes. Such an approach allows simpler and faster encoding/decoding
Arithmetic_coding
Entropy encoding
Examples of unary code uses include: In Golomb Rice code, unary encoding is used to encode the quotient part of the Golomb code word. In UTF-8, unary encoding
Unary_coding
Sequence where any order is equally likely
Ewens's sampling formula — a connection with population genetics Faro shuffle Golomb–Dickman constant Random permutation statistics Shuffling algorithms — random
Random_permutation
Mathematics concept
A Hadamard matrix of this order was found using a computer by Baumert, Golomb, and Hall in 1962 at JPL. They used a construction, due to Williamson, that
Hadamard_matrix
formula Exponential function Exponential generating function Exponential-Golomb coding Exponential growth Exponential hierarchy Exponential integral Exponential
List_of_exponential_topics
Shape formed from isosceles right triangles
rectangle. Polyaboloes of order 2 are also easily recognisable. Solomon W. Golomb found polyaboloes, including a triabolo, of order 8. Michael Reid found
Polyabolo
objects in two different ways). The proof given here is an adaptation of Golomb's proof. To keep things simple, let us assume that a is a positive integer
Proofs of Fermat's little theorem
Proofs_of_Fermat's_little_theorem
University of Southern California engineering school
Pseudorandom sequences/shift register sequences — in 1967, Prof. Solomon Golomb published the first book devoted exclusively to pseudorandom sequences Reed-Solomon
USC Viterbi School of Engineering
USC_Viterbi_School_of_Engineering
American mathematician (1927–2010)
William F.; Rodriguez, R. S.; Sherwood, H.; Reznick, Bruce A.; Rubel, Lee A.; Golomb, Solomon W.; Kinnon, Nick M.; Erdos, Paul; Selfridge, John (1988). "Problems
John_Selfridge
Widely used standard for video compression
elements not coded by CABAC or CAVLC, referred to as Exponential-Golomb coding (or Exp-Golomb). Loss resilience features including: A Network Abstraction Layer
Advanced_Video_Coding
Unary numbering is used as part of some data compression algorithms such as Golomb coding. It also forms the basis for the Peano axioms for formalizing arithmetic
List_of_numeral_systems
Geometric shape formed from nine squares
rightmost in the top row) and is the smallest polyomino with such a hole. Golomb, Solomon W. (1994). Polyominoes (2nd ed.). Princeton, New Jersey: Princeton
Nonomino
Dramatic Roles Archived 2015-04-06 at the Wayback Machine bach.nau.edu Uri Golomb: Academia.Edu Liturgical drama in Bach's St. Matthew Passion Goldberg Early
St_Matthew_Passion_structure
Data structure for approximate set membership
} is the requested false positive rate. The sequence of values is then sorted and compressed using Golomb coding (or some other compression technique)
Bloom_filter
Channel access method used by various radio communication technologies
35–43. Wikimedia Commons has media related to CDMA. Talk at Princeton Institute for Advanced Study on Solomon Golomb's work on pseudorandom sequences
Code-division_multiple_access
Approach to mathematics using computation
new periodic paths. distributed.net's OGR project searched for optimal Golomb rulers. The PrimeGrid project is searching for the smallest Riesel and Sierpiński
Experimental_mathematics
Mathematics problem
prisoners problem Unexpected hanging paradox Random permutation statistics Golomb–Dickman constant Philippe Flajolet, Robert Sedgewick (2009), Analytic Combinatorics
100_prisoners_problem
Encoding of negative numbers in binary number systems
Efficiency Video Coding/H.265 video compression standards to extend exponential-Golomb coding to negative numbers. In that extension, the least significant bit
Signed_number_representations
Points and lines with equal incidences
configuration exists for all p ≥ 2 ℓk + 1, where ℓk is the length of an optimal Golomb ruler of order k. The concept of a configuration may be generalized to higher
Configuration_(geometry)
Probability distribution
independent random variables whose probability distributions are indecomposable. Golomb coding is the optimal prefix code[clarification needed] for the geometric
Geometric_distribution
Paper-and-pencil game for two players
Conference on Artificial Intelligence. Springer. p. 735. ISBN 978-3-319-13560-1. Golomb, Solomon W.; Hales, Alfred W. (2002). "Hypercube tic-tac-toe" (PDF). More
Tic-tac-toe
American mathematician
"Sol Golomb--my friend and mentor" (PDF). Asia Pacific Mathematics Newsletter. 7 (1): 30–35. Retrieved June 14, 2023. Shift Register Sequences, Solomon
Alfred_W._Hales
Computer technology
well in encoding silence as silent intervals often consist of repeated sequences of identical samples. The reduction of identical samples stored subsequently
Silence_compression
In mathematics, invariant of square matrices
commute. Based on the diagram http://i.sstatic.net/gCaz3.png by Solomon W. Golomb that appeared in Mathematics Magazine, March 1985, altered to avoid overlapping
Determinant
File format for block-based Gzip compression
is a core component of the common BAM format (the binary version of the Sequence Alignment Map format) and is also used to compress and index Variant Call
BGZF
Hungarian mathematician (1913–1996)
"mathscinet/collaborationDistance". ams.org. Retrieved 2 December 2017. Michael Golomb. "Obituary of Paul Erdös at Purdue". www.math.purdue.edu. Retrieved 4 May
Paul_Erdős
American mathematician
1961, Solomon W. Golomb hired him to lead the Information Processing Group at JPL. He led the group for 10 years and then, after a sequence of positions in
Ed_Posner
Unlucky day in popular superstition
Mathematical Astronomy Morsels IV. p. 367. Golomb, Solomon (September 2007). "Solutions to 'Calendar oddities'". Golomb's Gambits. Johns Hopkins Magazine. Vol
Friday_the_13th
only prime number preceding a cube. 8, the largest cube in the Fibonacci sequence. 9, the first odd number that is composite. 10, the base of the decimal
List_of_numbers
American film composer
& Stone". www.tickettailor.com. Retrieved September 22, 2025. "Meet Ben Golomb | Musician & Filmmaker – SHOUTOUT LA". shoutoutla.com. Retrieved September
Chanda_Dancy
Musical work by Johann Sebastian Bach
Collaborative Hypertext "Johann Sebastian Bach's The Art of Fugue", article Uri Golomb, published in Goldberg Early Music Magazine Electronic realization by Klangspiegel
The_Art_of_Fugue
Form of entertainment in mathematics
Recreational Mathematics, author of Mathematics on Vacation. Solomon W. Golomb Golomb 1932 2016 American Mathematician and engineer, best known as the inventor
Recreational_mathematics
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Bibcode:2012ITSP...60.2180S. doi:10.1109/TSP.2012.2186134. Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication
Autocorrelation
Graphic novel series by Marjane Satrapi
to the intense political events happening in the story. Professor Liorah Golomb from the University of Oklahoma states about Persepolis and related books;
Persepolis_(comics)
"Qubic: 4 x 4 x 4 Tic-Tac-Toe", Mathematical Magazine 53 (1980) 202–216. Golomb, Solomon W.; Hales, Alfred W. (2002), "Hypercube tic-tac-toe", More games
Tic-tac-toe_variants
Array data structure that compactly stores bits
n {\displaystyle {\frac {1}{2^{n}}}} . This is also the special case of Golomb coding where the parameter M {\displaystyle M} is 1; this parameter is only
Bit_array
Technique to compress data
symbols, which are then encoded. For the simple case of Bernoulli processes, Golomb coding is optimal among prefix codes for coding run length, a fact proved
Huffman_coding
Mechanically-interlinked pieces to be manipulated
certain shape. The Soma cube made by Piet Hein, the Pentomino by Solomon Golomb and the aforementioned laying puzzles Tangram and "Anker-puzzles" are all
Mechanical_puzzle
Journal. 11 (1): 65–81. doi:10.1215/S0012-7094-44-01108-7. MR 0009590. Golomb, Solomon W.; Baumert, Leonard D. (1963). "The Search for Hadamard Matrices"
Williamson_conjecture
15th-century Inca citadel in Peru
Astete 2020a, p. 313. Spizzichino et al. 2022, pp. 16–19. Hearn, Kelly; Golomb, Jason (21 January 2017). "Machu Picchu". National Geographic. Retrieved
Machu_Picchu
American cartoonist (born 1986)
influential female independent and underground comic creators by Liorah Golomb. The webcomic won the second Queer Press Grant from Prism Comics which allowed
Ro_Salarian
problem "semicrosses", and they were also called Stein corners by Solomon W. Golomb. A collection of disjoint tripods can be represented compactly as a monotonic
Tripod_packing
Strategy board game
the center of the board to win. Cheskers: A variant invented by Solomon Golomb. Each player begins with a bishop and a camel (which jumps with coordinates
Checkers
American mathematician (1940–1999)
ISBN 9781468466867 (electronic book) Polyominoes by Gill Barequet, Solomon W. Golomb, and David A. Klarner, December 2016 The number of tilings of a block with
David_A._Klarner
History podcast and website
Retrieved January 18, 2018. Conway's RATS Sequence Futility Closet: Science & Math, March 30, 2017 Golomb Rulers Futility Closet: Science & Math, November
Futility_Closet
Geometric graph with unit edge lengths
only wheel graph that is a unit distance graph), and the Moser spindle and Golomb graph (small 4-chromatic unit distance graphs). All generalized Petersen
Unit_distance_graph
Series of books
curves (conic sections and cycloids Golomb Rulers, four-dimensional "Tic Tac Toe", The Golden Ratio, Fibonacci sequence, Logarithmic spirals, musical ratios
Murderous_Maths
Neuropsychiatric disorder
1002/ana.410190405. PMID 3707085. S2CID 46441945. Scepkowski, Lisa A.; Cronin-Golomb, Alice (2003). "The Alien Hand: Cases, Categorizations, and Anatomical Correlates"
Alien_hand_syndrome
Abstract strategy game
August 6, 2023 – via Internet Archive. Tic-tac-toe game on the cube 3×3×3 Golomb, Solomon W.; Hales, Alfred W. (August 2002). "Hypercube Tic-Tac-Toe". In
3D_tic-tac-toe
Type of behavior of a dynamical system
pentagons can be joined to make one with twice the dimensions. Solomon W. Golomb coined the term rep-tiles for self-replicating tilings. In 2012, Lee Sallows
Self-replication
English songwriter ("Callow-la-vita", "Big Ship", "Rachel") and singer. Jacob Golomb, 76, Israeli philosopher. Dorothy Goodman, 97, American educator, heart
Deaths_in_July_2023
Video compression format, succeeds H.264/MPEG-4 AVC
"Reduced-Complexity Entropy Coding of Transform Coefficient Levels Using Truncated Golomb-Rice Codes in Video Compression" (PDF). Gary Sullivan; Jens-Rainer Ohm (October
High_Efficiency_Video_Coding
German philosopher (1844–1900)
Routledge. ISBN 0415911478. Jacob, Golomb (2004). Nietzsche and Zion. Cornell University Press. ISBN 978-0801437625. Jacob, Golomb. Nietzsche and Zion. Ohana
Friedrich_Nietzsche
Transposition table Black path game Sylver coinage Generating function Golomb coding Golomb ruler Graeco-Latin square Gray code Hadamard matrices Complex Hadamard
Index of combinatorics articles
Index_of_combinatorics_articles
Class of enzymes
S2CID 207065284. Groner Y, Elroy-Stein O, Avraham KB, Schickler M, Knobler H, Minc-Golomb D, et al. (1994). "Cell damage by excess CuZnSOD and Down's syndrome". Biomedicine
Superoxide_dismutase
Letter that is not pronounced
(phonology) Three-letter rule, the source of some common English silent letters. Golomb, Solomon (2021-03-12). "Silent letters". Johns Hopkins Magazine (Hub). Johns
Silent_letter
Technique used in signal processing and data compression
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies
Discrete_cosine_transform
a computational approach. Cambridge University Press, 2012. Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication
Waveform_shaping
travel, tourism, insurance
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travel, tourism, insurance