论文标题
边缘理想不变链的渐近规则性
Asymptotic regularity of invariant chains of edge ideals
论文作者
论文摘要
我们研究了非零边缘理想的链条，这些链条是在积极整数上增加功能的MONOID $ \ MATHRM {INC} $不变的。 We prove that the sequence of Castelnuovo--Mumford regularity of ideals in such a chain is eventually constant with limit either 2 or 3, and we determine explicitly when the constancy behaviour sets in. This provides further evidence to a conjecture on the asymptotic linearity of the regularity of $\mathrm{Inc}$-invariant chains of homogeneous ideals.这些证明揭示了$ \ mathrm {inc} $的意外组合属性 - 边缘理想的不变链。
We study chains of nonzero edge ideals that are invariant under the action of the monoid $\mathrm{Inc}$ of increasing functions on the positive integers. We prove that the sequence of Castelnuovo--Mumford regularity of ideals in such a chain is eventually constant with limit either 2 or 3, and we determine explicitly when the constancy behaviour sets in. This provides further evidence to a conjecture on the asymptotic linearity of the regularity of $\mathrm{Inc}$-invariant chains of homogeneous ideals. The proofs reveal unexpected combinatorial properties of $\mathrm{Inc}$-invariant chains of edge ideals.
