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A linear code over a finite field with q elements F_q is a linear subspace C subset F_q^n. The vectors forming the subspace are called codewords. When codewords are chosen ...

In abstract topology, a machine is method for producing infinite loop spaces and spectra. In automata theory, an abstract machine that is implemented in hardware is simply ...

Let (A,<=) be a partially ordered set. Then an element m in A is said to be maximal if, for all a in A, m!<=a. Alternatively, an element m in A is maximal such that if m<=a ...

The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

Given a collection of sets, a member set that is not a proper subset of another member set is called a minimal set. Minimal sets are important in graph theory, since many ...

A morphism f:Y->X in a category is a monomorphism if, for any two morphisms u,v:Z->Y, fu=fv implies that u=v. In the categories of sets, groups, modules, etc., a monomorphism ...

The mutual information between two discrete random variables X and Y is defined to be I(X;Y)=sum_(x in X)sum_(y in Y)P(x,y)log_2((P(x,y))/(P(x)P(y))) (1) bits. Additional ...

A theorem in game theory which guarantees the existence of a set of mixed strategies for finite, noncooperative games of two or more players in which no player can improve ...

A natural transformation Phi={Phi_C:F(C)->D(C)} between functors F,G:C->D of categories C and D is said to be a natural isomorphism if each of the components is an ...

A group G is nilpotent if the upper central sequence 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n=G for some n. Nilpotent groups have the property that ...