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A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted |X| or ...

In mathematics, a formal language is normally defined by an alphabet and formation rules. The alphabet of a formal language is a set of symbols on which this language is ...

A free idempotent monoid is a monoid that satisfies the identity x^2=x and is generated by a set of elements. If the generating set of such a monoid is finite, then so is the ...

An extension of two-valued logic such that statements need not be true or false, but may have a degree of truth between 0 and 1. Such a system can be extremely useful in ...

The Golay code is a perfect linear error-correcting code. There are two essentially distinct versions of the Golay code: a binary version and a ternary version. The binary ...

The graph diameter of a graph is the length max_(u,v)d(u,v) of the "longest shortest path" (i.e., the longest graph geodesic) between any two graph vertices (u,v), where ...

The graph strong product, also known as the graph AND product or graph normal product, is a graph product variously denoted G□AdjustmentBox[x, BoxMargins -> {{-0.65, ...

A Hamiltonian walk on a connected graph is a closed walk of minimal length which visits every vertex of a graph (and may visit vertices and edges multiple times). For ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. For example, in the field of rational polynomials Q[x] (i.e., ...