# On the $h$-vector of ($S_r$) simplicial complexes

## TL;DR

This paper investigates the properties of the $h$-vector in ($S_r$) simplicial complexes and provides a negative answer to a previously posed question about its characteristics.

## Contribution

It offers the first counterexample or negative result concerning the $h$-vector of ($S_r$) simplicial complexes, challenging prior assumptions.

## Key findings

- Provided a negative answer to a question about the $h$-vector.
- Challenged existing beliefs about ($S_r$) simplicial complexes.
- Contributed to the understanding of the limitations of $h$-vector properties.

## Abstract

We give a negative answer to a question proposed in [3], regarding the $h$-vector of ($S_r$) simplicial complexes.