From Monomials to Words to graphs

Details From Monomials to Words to graphs From Monomials to Words to graphs

2003-02-20

arxiv.org/abs/math/0302252v1

Mathematics

Commutative Algebra

27 pages, 2 postscript figures, uses gastex.sty

Scientific paper

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 <\sigma(I)> generated by \sigma(I) in the free monoid is finitely generated. Whether there exists an ordering such that <\sigma(I)> is finitely generated turns out to be NP-complete. The latter problem is closely related to the recognition problem for comparability graphs.

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