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Let L denote the partition lattice of the set {1,2,...,n}. The maximum element of L is M={{1,2,...,n}} (1) and the minimum element is m={{1},{2},...,{n}}. (2) Let Z_n denote ...

A Steiner system S(t,k,v) is a set X of v points, and a collection of subsets of X of size k (called blocks), such that any t points of X are in exactly one of the blocks. ...

An n-tuple, sometimes simply called a "tuple" when the number n is known implicitly, is another word for a list, i.e., an ordered set of n elements. It can be interpreted as ...

A hash function H projects a value from a set with many (or even an infinite number of) members to a value from a set with a fixed number of (fewer) members. Hash functions ...

The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix. The set of eigenvalues of a graph is called a graph spectrum. The largest eigenvalue ...

Let S be a set and F={S_1,...,S_p} a nonempty family of distinct nonempty subsets of S whose union is union _(i=1)^pS_i=S. The intersection graph of F is denoted Omega(F) and ...

The kth power of a graph G is a graph with the same set of vertices as G and an edge between two vertices iff there is a path of length at most k between them (Skiena 1990, ...

A vertex-induced subgraph (sometimes simply called an "induced subgraph") is a subset of the vertices of a graph G together with any edges whose endpoints are both in this ...

An algorithm for partitioning (or clustering) N data points into K disjoint subsets S_j containing N_j data points so as to minimize the sum-of-squares criterion ...

A graph with projective plane crossing number equal to 0 may be said to be projective planar. Examples of projective planar graphs with graph crossing number >=2 include the ...