From Monomials to Words to graphs

Abstract

Given a finite alphabet X and an ordering on the letters, the map \sigma sends each monomial on X to the word that is the ordered product of the letter powers in the monomial. Motivated by a question on Groebner bases, we characterize ideals I in the free commutative monoid (in terms of a generating set) such that the ideal generated by \sigma(I) in the free monoid is finitely generated. Whether there exists an ordering such that is finitely generated turns out to be NP-complete. The latter problem is closely related to the recognition problem for comparability graphs.Comment: 27 pages, 2 postscript figures, uses gastex.st