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One of the Zermelo-Fraenkel axioms which asserts the existence for any set a of the power set x consisting of all the subsets of a. The axiom may be stated symbolically as ...

The term Borel hierarchy is used to describe a collection of subsets of R defined inductively as follows: Level one consists of all open and closed subsets of R, and upon ...

The (weak) Bruhat graph B_n of order n is the simple graph having have all permutations of {1,2,...,n} as vertices, and with an edge between pairs of permutations that differ ...

The finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special ...

A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...

A group generated by the elements P_i for i=1, ..., n subject to (P_iP_j)^(M_(ij))=1, where M_(ij) are the elements of a Coxeter matrix. Coxeter used the notation [3^(p,q,r)] ...

A cyclic graph is a graph containing at least one graph cycle. A graph that is not cyclic is said to be acyclic. A cyclic graph possessing exactly one (undirected, simple) ...

A set is denumerable iff it is equipollent to the finite ordinal numbers. (Moore 1982, p. 6; Rubin 1967, p. 107; Suppes 1972, pp. 151-152). However, Ciesielski (1997, p. 64) ...

The Doro graph is a distance-transitive and Distance-Regular Graph on 68 vertices and with valency 12. It is the unique automorphic graph having intersection array ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...