Given any finite simplicial complex $\Delta$, we show how to construct from a colouring $\chi$ of $\Delta$ a new simplicial complex $\Delta_{\chi}$ that is balanced and vertex decomposable. In addition, the $h$-vector of $\Delta_{\chi}$ is precisely the $f$-vector of $\Delta$. Our construction generalizes the "whiskering'' construction of Villarreal, and Cook and Nagel. We also reverse this construction to prove a special case of a conjecture of Cook and Nagel, and Constantinescu and Varbaro on the $h$-vectors of flag complexes.
@article{10_37236_2552,
author = {Jennifer Biermann and Adam Van Tuyl},
title = {Balanced vertex decomposable simplicial complexes and their \(h\)-vectors},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {3},
doi = {10.37236/2552},
zbl = {1298.05332},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2552/}
}
TY - JOUR
AU - Jennifer Biermann
AU - Adam Van Tuyl
TI - Balanced vertex decomposable simplicial complexes and their \(h\)-vectors
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/2552/
DO - 10.37236/2552
ID - 10_37236_2552
ER -
%0 Journal Article
%A Jennifer Biermann
%A Adam Van Tuyl
%T Balanced vertex decomposable simplicial complexes and their \(h\)-vectors
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/2552/
%R 10.37236/2552
%F 10_37236_2552
Jennifer Biermann; Adam Van Tuyl. Balanced vertex decomposable simplicial complexes and their \(h\)-vectors. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/2552
