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From Monomials to Words to graphs

Cristina G. Fernandes·Edward L. Green·Arnaldo Mandel
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Abstract

Given a finite alphabet X and an ordering on the letters, the map σsends 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 <σ(I)> generated by σ(I) in the free monoid is finitely generated. Whether there exists an ordering such that <σ(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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Cristina G. Fernandes, Edward L. Green, Arnaldo Mandel. 2003-02-20. From Monomials to Words to graphs. https://arxiv.org/abs/math/0302252

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