On the complete cd-index of a Bruhat interval
Combinatorics
2012-06-01 v2
Abstract
We study the non-negativity conjecture of the complete cd-index of a Bruhat interval defined by Billera and Brenti. For each cd-monomial M we construct a set of paths, such that if a "flip condition" is satisfied, then the number of these paths is the coefficient of the monomial M in the complete cd-index. When the monomial contains at most one d, then the condition follows from Dyer's proof of Cellini's conjecture. Hence the coefficients of these monomials are non-negative. We also relate the flip condition to shelling of Bruhat intervals.
Cite
@article{arxiv.1201.5161,
title = {On the complete cd-index of a Bruhat interval},
author = {Kalle Karu},
journal= {arXiv preprint arXiv:1201.5161},
year = {2012}
}
Comments
13 pages, 1 figure