\(h^\ast\)-vectors, Eulerian polynomials and stable polytopes of graphs
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
Conditions are given on a lattice polytope $P$ of dimension $m$ or its associated affine semigroup ring which imply inequalities for the $h^*$-vector $(h^*_0, h^*_1,\dots,h^*_m)$ of $P$ of the form $h^*_i \ge h^*_{d-i}$ for $1 \le i \le \lfloor d / 2 \rfloor$ and $h^*_{\lfloor d / 2 \rfloor} \ge h^*_{\lfloor d / 2 \rfloor + 1} \ge \cdots \ge h^*_d$, where $h^*_i = 0$ for $d < i \le m$. Two applications to order polytopes of posets and stable polytopes of perfect graphs are included.
DOI :
10.37236/1863
Classification :
52B20, 06A11, 05C17, 05E99
Mots-clés : lattice polytope, Ehrhart polynomial, regular triangulation, order polytope, perfect graph
Mots-clés : lattice polytope, Ehrhart polynomial, regular triangulation, order polytope, perfect graph
@article{10_37236_1863,
author = {Christos A. Athanasiadis},
title = {\(h^\ast\)-vectors, {Eulerian} polynomials and stable polytopes of graphs},
journal = {The electronic journal of combinatorics},
year = {2004},
volume = {11},
number = {2},
doi = {10.37236/1863},
zbl = {1068.52016},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1863/}
}
Christos A. Athanasiadis. \(h^\ast\)-vectors, Eulerian polynomials and stable polytopes of graphs. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1863
Cité par Sources :