The CDE property for skew vexillary permutations
arXiv:1811.02404 · doi:10.1016/j.jcta.2019.06.005
Abstract
We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree expectations (CDE) property. Actually our theorem applies more generally to certain "skew vexillary" permutations (a notion we introduce), and shows that these posets are in fact "toggle CDE." As a corollary we obtain a homomesy result for rowmotion acting on semidistributive lattices in the sense of Barnard and of Thomas and Williams.
arXiv comment51 pages, 15 figures; v2: updated to include discussion of refined homomesies for full weak order, v3: forthcoming, JCTA
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