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Castelnuovo-Mumford regularity for $321$-avoiding Kazhdan-Lusztig varieties (2308.14208v1)
Published 27 Aug 2023 in math.CO and math.AC
Abstract: We introduce an algorithm which combinatorially computes the Castelnuovo-Mumford regularity of 321-avoiding Kazhdan-Lusztig varieties using excited diagrams. This extends earlier work of Rajchgot, Weigandt, and the author (2022) which computes the regularity of Grassmannian Kazhdan-Lusztig varieties. Our results specialize to compute the regularity of all two-sided mixed ladder determinantal varieties in terms of lattice paths.