Castelnuovo-Mumford regularity for $321$-avoiding Kazhdan-Lusztig varieties
Combinatorics
2025-09-15 v2 Commutative Algebra
Abstract
We prove the Castelnuovo--Mumford regularity of 321-avoiding Kazhdan--Lusztig varieties can be computed combinatorially in terms of -theoretic skew excited Young diagrams. We present an algorithm which gives a lower bound for this regularity and describe a setting in which this algorithm provides precise regularity computations. This algorithm specializes to compute the regularity of all two-sided mixed ladder determinantal varieties.
Keywords
Cite
@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}
}
Comments
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