Balanced vertex decomposable simplicial complexes and their hvectors
Abstract
Given any finite simplicial complex \Delta, we show how to construct a new simplicial complex \Delta_{\chi} that is balanced and vertex decomposable. Moreover, we show that the hvector of the simplicial complex \Delta_{\chi} is precisely the fvector, denoted f(\Delta), of the original complex \Delta. We deduce this result by relating f(\Delta) with the graded Betti numbers of the Alexander dual of \Delta_{\chi}. Our construction generalizes the "whiskering" construction of Villarreal, and Cook and Nagel. As a corollary of our work, we add a new equivalent statement to a theorem of Björner, Frankl, and Stanley that classifies the fvectors of simplicial complexes. We also prove a special case of a conjecture of Cook and Nagel, and Constantinescu and Varbaro on the hvectors of flag complexes.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 arXiv:
 arXiv:1202.0044
 Bibcode:
 2012arXiv1202.0044B
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics;
 05E45;
 05A15;
 13F55
 EPrint:
 16 pages