Balanced Vertex Decomposable Simplicial Complexes and their h-vectors

摘要

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.