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Difference set

In combinatorics, a ( v , k , λ ) {\displaystyle (v,k,\lambda )} difference set is a subset D {\displaystyle D} of size k {\displaystyle k} of a group G {\displaystyle G} of order v {\displaystyle v} such that every non-identity element of G {\displaystyle G} can be expressed as a product d 1 d 2 − 1 {\displaystyle d_{1}d_{2}^{-1}} of elements of D…

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Overview

Basic facts

Equivalent and isomorphic difference sets

Multipliers

Ryser and Lander conjectures

Parameters

Selected constructions

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Application

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Difference set

Nodes43
Edges42
Triples105
Avg. degree1.95
Density0.046512
Components1

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Difference set

Top relations

related to Further reading · 35
Difference set → Achieving, AMS, Chicago, Combinatorics, Connecting Algebra, CRC Press, CRC Standard Mathematical Tables, Cyclotomy, Daniel, Difference Sets, EH, Formulae, Geometry, Georgios, Giannakis, HSK, IEEE Transactions, Information Theory, ISBN, ISSN
related to Parameters · 14
Difference set → Chen, Davis, Difference, Hadamard, Jedwab, Known, McFarland, Menon, Paley-type, Ryser's, Some, Spence, The, These
related to Basic facts · 13
Difference set → An, Any, Bruck, Chowla, Each, Fano, If, In, It, Not, Ryser, Since, The
related to Ryser and Lander conjectures · 11
Difference set → Eric, For, Hadamard, In, It, Lander, Lander's, Menon, Ryser's, Since, Sylow
related to history · 7
Difference set → Bose, Bruck, However, Marshall Hall Jr, Multipliers, Paley Difference Sets, The
related to Multipliers · 7
Difference set → First Multiplier Theorem, Hall, If, Later, Second Multiplier Theorem, The, This
related to Selected constructions · 5
Difference set → Galois, GF, In, Paley, The
related to Application · 4
Difference set → Giannakis, Welch, Xia, Zhou
related to Equivalent and isomorphic difference sets · 4
Difference set → Equivalent, In, The, Two
is a · 3
Difference set → difference family with s, power of a prime greater than 3, subset D

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Important terminology

difference displaystyle set group lambda sets prime order conjecture called every -difference cyclic elements integer abelian parameters multiplier -1 isbn

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Difference setis asubset D0.90text
Difference setis apower of a prime greater than 30.90text
Difference setis adifference family with s0.90text
Difference setrelated to ApplicationXia0.60section
Difference setrelated to ApplicationZhou0.60section
Difference setrelated to ApplicationGiannakis0.60section
Difference setrelated to ApplicationWelch0.60section
Difference setrelated to Basic factsThe0.60section
Difference setrelated to Basic factsIf0.60section
Difference setrelated to Basic factsIn0.60section
Difference setrelated to Basic factsEach0.60section
Difference setrelated to Basic factsAny0.60section

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