Recently, Benedetti et al. introduced an Ehrhart-like polynomial associated to a graph. This polynomial is defined as the volume of a certain flow polytope related to a graph and has the property that the leading coefficient is the volume of the flow polytope of the original graph with net flow vector $(1,1,\dots,1)$. Benedetti et al. conjectured a formula for the Ehrhart-like polynomial of what they call a caracol graph. In this paper their conjecture is proved using constant term identities, labeled Dyck paths, and a cyclic lemma.
@article{10_37236_9187,
author = {Jihyeug Jang and Jang Soo Kim},
title = {Volumes of flow polytopes related to caracol graphs},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {4},
doi = {10.37236/9187},
zbl = {1451.05012},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9187/}
}
TY - JOUR
AU - Jihyeug Jang
AU - Jang Soo Kim
TI - Volumes of flow polytopes related to caracol graphs
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/9187/
DO - 10.37236/9187
ID - 10_37236_9187
ER -
%0 Journal Article
%A Jihyeug Jang
%A Jang Soo Kim
%T Volumes of flow polytopes related to caracol graphs
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/9187/
%R 10.37236/9187
%F 10_37236_9187
Jihyeug Jang; Jang Soo Kim. Volumes of flow polytopes related to caracol graphs. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9187
