Séminaire Lotharingien de Combinatoire, 86B.41 (2022), 12 pp.
Ezgi Kantarcı Oğuz and Mohan Ravichandran
Ideal Lattices of Fence Posets and Rank Unimodality
Abstract.
We prove a conjecture of Morier-Genoud and Ovsienko that says that rank polynomials of the distributive lattices of lower ideals of fence posets are unimodal. We do this by introducing a related class of circular fence posets and proving a stronger version of the conjecture due to
McConville, Sagan and Smyth. We show that the rank polynomials of circular fence posets are symmetric and conjecture that unimodality holds except in some particular cases. We also apply the recent work of Elizalde, Plante, Roby and Sagan on rowmotion on fences and show many of their homomesy results hold for the circular case as well.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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