From Monomials to Words to graphs
交换代数
2007-05-23 v1 组合数学
群论
摘要
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.
引用
@article{arxiv.math/0302252,
title = {From Monomials to Words to graphs},
author = {Cristina G. Fernandes and Edward L. Green and Arnaldo Mandel},
journal= {arXiv preprint arXiv:math/0302252},
year = {2007}
}
备注
27 pages, 2 postscript figures, uses gastex.sty