f-vectors and h-vectors of simplicial posets
نویسنده
چکیده
Stanely, R.P., f-vectors and h-vectors of simplicial posets, Journal of Pure and Applied Algebra 71 (1991) 319-331. A simplicial poset is a (finite) poset P with d such that every interval [6, x] is a boolean algebra. Simplicial posets are generalizations of simplicial complexes. The f-vector f(P) = (f,, f,, , ,f_,) of a simplicial poset P of rank d is defined by f; = #{x E P: [6, x] g B,, I}, where B,,, 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 pose&, and an almost complete characterization for Gorenstein simplicial posets. The Cohen-Macaulay case relies on the theory of algebras with straightening laws (ASL’s).
منابع مشابه
f - vectors of simplicial posets that are balls
Results of R. Stanley and M. Masuda completely characterize the hvectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vectors. We also present new methods for constructing poset balls with specific h-...
متن کاملSUBDIVISIONS AND LOCAL h-VECTORS
In Part I a general theory of f-vectors of simplicial subdivisions (ortriangulations) of simplicial complexes is developed, based on the concept of lo-cal h-vector. As an application, we prove that the h-vector of a Cohen-Macaulaycomplex increases under "quasi-geometric" subdivision, thus establishing a spe-cial case of a conjecture of Kalai and this author. Techniques include c...
متن کاملLinear Inequalities for Enumerating Chains in Partially Ordered Sets
We characterize the linear inequalities satisfied by flag f -vectors of all finite bounded posets. We do the same for semipure posets. In particular, the closed convex cone generated by flag f -vectors of bounded posets of fixed rank is shown to be simplicial, and the closed cone generated by flag f -vectors of semipure posets of fixed rank is shown to be polyhedral. The extreme rays of both of...
متن کاملTwo Decompositions in Topological Combinatorics with Applications to Matroid Complexes
This paper introduces two new decomposition techniques which are related to the classical notion of shellability of simplicial complexes, and uses the existence of these decompositions to deduce certain numerical properties for an associated enumerative invariant. First, we introduce the notion of M-shellability, which is a generalization to pure posets of the property of shellability of simpli...
متن کاملA classification of the face numbers of Buchsbaum simplicial posets
The family of Buchsbaum simplicial posets generalizes the family of simplicial cell manifolds. The h′vector of a simplicial complex or simplicial poset encodes the combinatorial and topological data of its face numbers and the reduced Betti numbers of its geometric realization. Novik and Swartz showed that the h′-vector of a Buchsbaum simplicial poset satisfies certain simple inequalities. In t...
متن کامل