Article ID Journal Published Year Pages File Type
4595912 Journal of Pure and Applied Algebra 2015 11 Pages PDF
Abstract

In this paper we prove that every toric ideal associated with a gap-free graph G has a squarefree lexicographic initial ideal. Moreover, in the particular case when the complementary graph of G is chordal (i.e. when the edge ideal of G   has a linear resolution), we show that there exists a reduced Gröbner basis GG of the toric ideal of G   such that all the monomials in the support of GG are squarefree. Finally, we show (using work by Herzog and Hibi) that if I is a monomial ideal generated in degree 2, then I has a linear resolution if and only if all powers of I have linear quotients, thus extending a result by Herzog, Hibi and Zheng.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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