Search results

{{Short description|A subgroup of a group}} ...substituting group elements for variables in a given set of [[word (group theory)|words]]. ...

The discipline of [[combinatorial topology]] used combinatorial concepts in topology and in the early 20th century this turned into the fie ...r application of [[Homology (mathematics)|homological]] methods to [[graph theory]], Lovász proved both the undirected and directed versions of a [[conjectur ...

...eeb|de}} in 1972, it became part of the foundations of [[structural Ramsey theory]].{{r|glr72}} A special case of the Graham–Rothschild theorem motivates the ...ese wildcard characters. A combinatorial cube of dimension one is called a combinatorial line.{{r|lnka}} ...

{{Short description|Topological graph theory}} ...e named for Stephen E. Wilson, who published them for [[regular map (graph theory)|regular maps]] in 1979;{{r|w}} they were extended to all cellular graph em ...

...977,<ref>S. Toida: "A note on Adam's conjecture", Journal of Combinatorial Theory (B), pp. 239–246, October–December 1977</ref> is a refinement of the dispro ...set <math>S</math>. Every [[group automorphism|symmetry]] of the [[cyclic group]] of addition modulo <math>n</math> ...

...subcubes of a given combinatorial cube. They have applications in [[Ramsey theory]] and in computer science in the detection of [[duplicate code]]. ...led its dimension. A one-dimensional combinatorial cube may be called a '''combinatorial line'''.{{r|lnka}} ...

...bgroup]] of''G''. The Schreier graph encodes the abstract structure of the group modulo an [[equivalence relation]] formed by the [[coset]]s of the subgroup ...eter |title=A practical method for enumerating cosets of a finite abstract group |journal=Proceedings of the Edinburgh Mathematical Society |volume=5 |issue ...

{{Short description|Theory in number theory}} ...ver ''X''. The first results for number fields and their [[Absolute Galois group|absolute Galois groups]] were obtained by [[Jürgen Neukirch]], [[Masatoshi ...

{{Short description|Identity in group theory}} ...ng process]], and implies that ''p''-groups of small class are [[regular p-group|regular]]. ...

...precise definitions of these are given below. As it turns out, for a free group and for the free product of groups, there exists a unique normal form i.e e Let <math>G</math> be a [[free group]] with [[generating set]] <math>S</math>. Each element in <math>G</math> is ...

{{Short description|Concept in combinatorial game theory}} In [[combinatorial game theory]], and particularly in the theory of [[impartial game]]s in [[misère]] play, an '''indistinguishability quoti ...

...abin]], [https://www.jstor.org/stable/1969933 ''Recursive unsolvability of group theoretic problems''], [[Annals of Mathematics]] (2), vol. 67, 1958, pp. 17 #''P'' is an abstract property, that is, ''P'' is preserved under [[group isomorphism]]. ...

...ó Babai|title=Spectra of Cayley graphs |journal=[[Journal of Combinatorial Theory, Series B]] |date=October 1979 |volume=27 |issue=2 |pages=180–189 |doi=10.1 ...ey graph|directed Cayley graph]]) corresponding to a [[Generating set of a group|generating subset]] <math>S</math> of <math>G\setminus \{1\}</math>, and l ...

...>; cf. [[Automorphism group#In category theory]].</ref> of the [[symmetric group]] <math>\mathbb{S}_n</math>.<!-- The notion is due to J.P.May. --> The category of [[combinatorial species]] is equivalent to the category of finite <math>\mathbb{S}</math>-s ...

The '''110-vertex Iofinova–Ivanov graph''' is, in [[graph theory]], a [[semi-symmetric graph|semi-symmetric]] [[cubic graph]] with 110 verti ...bic bipartite graphs whose automorphism groups act [[Primitive permutation group|primitively]] on each partition.<ref>{{cite web|last1=Han and Lu|title=Affi ...

In [[combinatorics|combinatorial]] mathematics, an '''Eulerian poset''' is a [[graded poset]] in which every * Let ''W'' be a [[Coxeter group]] with [[Bruhat order]]. Then (''W'',&le;) is an Eulerian poset. ...

...etric functions]] depending on a parameter ''t'' and a [[partition (number theory)|partition]] &lambda;. They are [[Schur polynomial|Schur functions]] when ...'') elements equal to ''i'', and ''S''_''n'' is the [[symmetric group]] of order ''n''!. ...

...mbinatorics]], [[ergodic theory]], [[analysis]], [[graph theory]], [[group theory]], and [[linear algebra|linear-algebra]]ic and polynomial methods. ...that ''{{Mvar|A}}'' and ''{{Mvar|B}}'' are finite subsets of the [[cyclic group]] {{Math|&integers;/''p''&integers;}} for a prime {{Mvar|p}}, then the foll ...

...n important role in [[algebraic combinatorics]] and [[geometric complexity theory]]. They were introduced by [[Francis Dominic Murnaghan (mathematician)|Murn ...om its relevance in the [[Geometric complexity theory|Geometric Complexity Theory]] program. ...

...ory of the symmetric group|irreducible character]] values of a [[symmetric group]].<ref>Richard Stanley, ''Enumerative Combinatorics, Vol. 2''</ref> There are several generalizations of this rule beyond the representation theory of symmetric groups, but they are not covered here. ...