论文标题
图形的曲折理想的规律性和h-多项式
Regularity and h-polynomials of toric ideals of graphs
论文作者
论文摘要
对于所有整数$ 4 \ leq r \ leq D $，我们证明存在有限的简单图$ g = g = g = g = g_ {r，d} $，带有折叠的理想$ i_g \ subset r $，使得$ r/i_g $ a i_g $ has（castelnuovo-mumford）正常$ r $ r $ r $ r $和$ h $ h $ h $ -polynomial of d $ $ d $。为了实现这一目标，我们确定了一个图的家族，以使相关的感谢您的理想的分级betti数量与其最初的理想和此外，此最初的理想具有线性商。作为推论，我们可以恢复hibi，higashitani，kimura和O'Keefe的结果，以比较图形理想的深度和尺寸。
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.
