Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4595912 | Journal of Pure and Applied Algebra | 2015 | 11 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alessio D'Alì,