F-VECTORS AND H-VECTORS OF SIMPLICIAL POSETS

[摘要] A simplicial poset is a (finite) poset P with 0-tripple-over-dot such that every interval [0-tripple-over-dot, x] is a boolean algebra. Simplicial posets are generalizations of simplicial complexes. The f-vector f(P) = (f0,...,f(d-1)) of a simplicial poset P of rank d is defined by f(i) = #{x is-an-element-of n P: [0-tripple-over-dot, x] approximately-equal-to B(i+1)}, where B(i+1) is a boolean algebra of rank i + 1. We give a complete characterization of the f-vectors of simplicial posets and of Cohen-Macaulay simplicial posets, and an almost complete characterization for Gorenstein simplicial posets. The Cohen-Macaulay case relies on the theory of algebras with straightening laws (ASL's).

[发布日期] 1991-05-31