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A perfect matching of a graph is a matching (i.e., an independent edge set) in which every vertex of the graph is incident to exactly one edge of the matching. A perfect ...

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...

Given a ring R with identity, the general linear group GL_n(R) is the group of n×n invertible matrices with elements in R. The general linear group GL_n(q) is the set of n×n ...

The set of left cosets of a subgroup H of a topological group G forms a topological space. Its topology is defined by the quotient topology from pi:G->G/H. Namely, the open ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

The edge count of a graph g, commonly denoted M(g) or E(g) and sometimes also called the edge number, is the number of edges in g. In other words, it is the cardinality of ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

Let union represent "or", intersection represent "and", and ^' represent "not." Then, for two logical units E and F, (E union F)^'=E^' intersection F^' (E intersection ...

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...

There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a ...