f-vectors of Simplicial Posets that are Balls

TL;DR

This paper characterizes the h-vectors of simplicial poset balls up to dimension six, extending previous work on spheres by developing new conditions and construction methods using face rings.

Contribution

It introduces new conditions and construction techniques for h-vectors of simplicial poset balls, completing the characterization up to dimension six.

Findings

Complete characterization of h-vectors for simplicial poset balls up to dimension six

Development of new methods for constructing poset balls with specific h-vectors

Extension of known results from spheres to balls using face ring techniques

Abstract

Results of R. Stanley and M. Masuda completely characterize the h-vectors 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-vectors. These results allow us to give a complete characterization of the h-vectors of simplicial poset balls up through dimension six.