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<span style="color:rgb(34, 34, 34);font-family:Arial, Helvetica, sans-serif;font-size:small;background-color:rgb(255, 255, 255);display:inline !important">Title: Rank Polynomials of Fence Posets are Unimodal</span></div>
<div style=""><font color="#222222" face="Arial, Helvetica, sans-serif" size="2"><br>
</font><span style="color: rgb(34, 34, 34); font-family: Arial, Helvetica, sans-serif; font-size: small; background-color: rgb(255, 255, 255);">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, <span>Sagan</span> 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 <span>Sagan</span> on rowmotion on fences and show many of their homomesy results hold for
the circular case as well (joint work with Mohan Ravichandran).</span><br>
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