论文信息 - Algorithms for Properties of Factor Semigroups on Graphs

Algorithms for Properties of Factor Semigroups on Graphs

A quiver is a labeled, directed multigraph with loops. The set of walks in a quiver forms a semigroup under concatenation if we augment the set with a 0 walk for nonsensical concatenations. Any finite set of walks allows us to define a factor semigroup in a natural and computable way. We give a linear time algorithm to determine whether the factor semigroup is finite or infinite. An algorithm for enumerating the elements of the factor semigroup is also given. Applications are found in the Gröbner basis theory of path algebras.

Lenwood S. Heath | Craig A. Struble

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