---
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.'
address: ' Satoshi Murai, Department of Mathematical Science, Faculty of Science, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8512, Japan. '
author:
- Satoshi Murai
title: '$h$-vectors of simplicial cell balls'
---

Introduction
============

A *simplicial poset* is a finite poset $P$ with a minimal element $\hat 0$ such that every interval $[\hat 0, \sigma]$ for $\sigma \in P$ is a Boolean algebra. A typical example of a simplicial poset is the face poset of a simplicial complex, but not all simplicial posets come from simplicial complexes. Simplicial posets are CW-posets. Thus for any simplicial poset $P$ there is a regular CW-complex $\Gamma(P)$ whose face poset is isomorphic to $P$ (see [@Bj pp. 8–9]). A simplicial poset $P$ (or a CW-complex $\Gamma(P)$) is called a *simplicial cell $d$-ball (respectively $d$-sphere)* if $\Gamma(P)$ is homeomorphic to a $d$-ball (respectively $d$-sphere). Kolins 