Rank Polynomials of Fence Posets are Unimodal
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ID: 283444
2021
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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.
| Reference Key |
ravichandran2021rank
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| Authors | Ezgi Kantarcı Oğuz; Mohan Ravichandran |
| Journal | arXiv |
| Year | 2021 |
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