From monomials to words to graphs
نویسندگان
چکیده
Given a finite alphabet X and an ordering ≺ on the letters, the map σ≺ 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 Gröbner 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 ≺ 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. Research MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997–4). Research partially supported by CNPq/NSF grant n. 910123/99 Research partially supported by CNPq/NSF grant n. 910123/99 and MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997–4). MSC Classification (2000): 13P10 (Primary), 68R15, 05C17, 16Z05, 68Q25
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 105 شماره
صفحات -
تاریخ انتشار 2004