On the structure of the lattice of noncrossing partitions
Discrete Mathematics
Decomposition theorem for the cd-index of Gorenstein* posets
Journal of Algebraic Combinatorics: An International Journal
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We define the shortest path poset SP(u,v) of a Bruhat interval [u,v], by considering the shortest u---v paths in the Bruhat graph of a Coxeter group W, where u,v驴W. We consider the case of SP(u,v) having a unique rising chain under a reflection order and show that in this case SP(u,v) is a Gorenstein驴 poset. This allows us to derive the nonnegativity of certain coefficients of the complete cd-index. We furthermore show that the shortest path poset of an irreducible, finite Coxeter group exhibits a symmetric chain decomposition.