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arXiv · 2003.07149

Regularity and h-polynomials of toric ideals of graphs

Giuseppe Favacchio·Graham Keiper·Adam Van Tuyl
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Abstract

For all integers $4 \leq r \leq d$, we show that there exists a finite simple graph $G= G_{r,d}$ with toric ideal $I_G \subset R$ such that $R/I_G$ has (Castelnuovo-Mumford) regularity $r$ and $h$-polynomial of degree $d$. To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and furthermore, this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O'Keefe that compares the depth and dimension of toric ideals of graphs.

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Giuseppe Favacchio, Graham Keiper, Adam Van Tuyl. 2020-03-16. Regularity and h-polynomials of toric ideals of graphs. https://arxiv.org/abs/2003.07149

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