避免 $321$ 模式的 Kazhdan-Lusztig 簇的 Castelnuovo-Mumford 正则性
组合数学
2025-09-15 v2 交换代数
摘要
我们证明避免 321 模式的 Kazhdan–Lusztig 簇的 Castelnuovo–Mumford 正则性可以用 -理论的斜激发 Young 图组合地计算。我们给出一个算法，给出该正则性的下界，并描述该算法能提供精确正则性计算的一种情形。该算法特化后可计算所有双侧混合阶梯行列式簇的正则性。
引用
@article{arxiv.2308.14208,
title = {Castelnuovo-Mumford regularity for $321$-avoiding Kazhdan-Lusztig varieties},
author = {Colleen Robichaux},
journal= {arXiv preprint arXiv:2308.14208},
year = {2025}
}
备注
25 pages; We thank the anonymous reviewer who noted errors in the earlier version of this manuscript. In this version, we amend our theorem statements and give an algorithm to compute regularies in restricted cases. For general 321-avoiding permutations, our algorithm provides a lower bound