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Regularity and ℎ-polynomials of toric ideals of graphs
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-07-29 , DOI: 10.1090/proc/15126 Giuseppe Favacchio , Graham Keiper , Adam Van Tuyl
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-07-29 , DOI: 10.1090/proc/15126 Giuseppe Favacchio , Graham Keiper , Adam Van Tuyl
Abstract:For all integers 
, we show that there exists a finite simple graph 
with toric ideal 
such that 
has (Castelnuovo-Mumford) regularity 
and 
-polynomial of degree 
. 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, that 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.
中文翻译：
图的复曲面理想的正则性和ℎ多项式
摘要：对于所有整数，我们表明存在一个具有复曲面理想的有限简单图，它具有（Castelnuovo-Mumford）正则性和-多项式- 。为实现此目标，我们确定了一系列图，以使相关的复曲面理想的分级Betti数与其初始理想相符，而且此初始理想具有线性商。作为推论，我们可以得到Hibi，Higashitani，Kimura和O'Keefe的结果，该结果比较了复曲面理想图的深度和尺寸。
更新日期：2020-09-02
, we show that there exists a finite simple graph with toric ideal such that has (Castelnuovo-Mumford) regularity and -polynomial of degree . 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, that 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. 中文翻译：
图的复曲面理想的正则性和ℎ多项式
摘要：对于所有整数，我们表明存在一个具有复曲面理想的有限简单图，它具有（Castelnuovo-Mumford）正则性和-多项式- 。为实现此目标，我们确定了一系列图，以使相关的复曲面理想的分级Betti数与其初始理想相符，而且此初始理想具有线性商。作为推论，我们可以得到Hibi，Higashitani，Kimura和O'Keefe的结果，该结果比较了复曲面理想图的深度和尺寸。
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