On the complete cd-index of a Bruhat interval

Details On the complete cd-index of a Bruhat interval On the complete cd-index of a Bruhat interval

2012-01-25

arxiv.org/abs/1201.5161v1

Mathematics

Combinatorics

12 pages

Scientific paper

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 give several equivalent formulations of the flip conditon.

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