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The transitive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same transitive closure as R. Thus aR^'b for any elements a and b of X, ...

A relation R on a set S is transitive provided that for all x, y and z in S such that xRy and yRz, we also have xRz.

The reflexive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same reflexive closure as R. Thus aR^'b for any elements a and b of X, ...

The transitive closure of a binary relation R on a set X is the minimal transitive relation R^' on X that contains R. Thus aR^'b for any elements a and b of X provided that ...

A graph G is transitive if any three vertices (x,y,z) such that edges (x,y),(y,z) in G imply (x,z) in G. Unlabeled transitive digraphs are called digraph topologies.

A system in which words (expressions) of a formal language can be transformed according to a finite set of rewrite rules is called a reduction system. While reduction systems ...

If a fixed point is added to each group of a special complete series, then the resulting series is complete.

The process of finding a reduced set of basis vectors for a given lattice having certain special properties. Lattice reduction algorithms are used in a number of modern ...

Horowitz reduction is used in indefinite integration to reduce a rational function into polynomial and logarithmic parts. The polynomial part is then trivially integrated, ...

A strict order > on the set of terms of a term rewriting system is called a reduction order if 1. The set of terms is well ordered with respect to >, that is, all its ...