We construct a family of shellings for the canonical triangulation of the order polytope of the zig-zag poset. This gives a new combinatorial interpretation for the coefficients in the numerator of the Ehrhart series of this order polytope in terms of the swap statistic on alternating permutations. We also offer an alternate proof of this result using the techniques of rank selection. Finally, we show that the sequence of coefficients of the numerator of this Ehrhart series is symmetric and unimodal.
@article{10_37236_11526,
author = {Jane Ivy Coons and Seth Sullivant},
title = {The \(h^\ast\)-polynomial of the order polytope of the zig-zag poset},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {2},
doi = {10.37236/11526},
zbl = {1517.05008},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11526/}
}
TY - JOUR
AU - Jane Ivy Coons
AU - Seth Sullivant
TI - The \(h^\ast\)-polynomial of the order polytope of the zig-zag poset
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/11526/
DO - 10.37236/11526
ID - 10_37236_11526
ER -
%0 Journal Article
%A Jane Ivy Coons
%A Seth Sullivant
%T The \(h^\ast\)-polynomial of the order polytope of the zig-zag poset
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/11526/
%R 10.37236/11526
%F 10_37236_11526
Jane Ivy Coons; Seth Sullivant. The \(h^\ast\)-polynomial of the order polytope of the zig-zag poset. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11526
