h-Vectors of simplicial cell balls

TL;DR

This paper extends previous work by Samuel Kolins to fully characterize all possible h-vectors of simplicial cell balls in any dimension, advancing the understanding of their combinatorial structure.

Contribution

It provides a complete characterization of h-vectors for simplicial cell balls across all dimensions, building on Kolins' earlier dimension-limited results.

Findings

Complete characterization of h-vectors in arbitrary dimensions

Extension of necessary and sufficient conditions

Advancement in combinatorial topology of simplicial complexes

Abstract

A simplicial cell ball is a simplicial poset whose geometric realization is homeomorphic to a ball. Recently, Samuel Kolins gave a series of necessary conditions and sufficient conditions on $h$-vectors of simplicial cell balls, and characterized them up to dimension 6. In this paper, we extend Kolins' results. We characterize all possible $h$-vectors of simplicial cell balls in arbitrary dimension.