h-vectors of Gorenstein* simplicial posets

Details h-vectors of Gorenstein* simplicial posets h-vectors of Gorenstein* simplicial posets

2003-05-14

arxiv.org/abs/math/0305203v3

Adv. Math. 194 (2005), 332--344

Mathematics

Combinatorics

12 pages

Scientific paper

As is well known, h-vectors of simple (or simplicial) convex polytopes are characterized. In fact, those h-vectors must satisfy Dehn-Sommerville equations and some other inequalities. Simple convex polytopes determine Gorenstein* simplicial posets and h-vectors are defined for simplicial posets. It is known that h-vectors of Gorenstein* simplicial posets must satisfy Dehn-Sommerville equations and that every component in the h-vectors must be non-negative. In this paper we will show that h-vectors of Gorenstein* simplicial posets must satisfy one more subtle condition conjectured by R. Stanley and complete characterization of those h-vectors. Our proof is purely algebraic but the idea of the proof stems from topology.

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