S-positivity of interval hypergraphs

TL;DR

This paper proves the s-positivity of chromatic functions for interval hypergraphs and confirms a related conjecture, also providing a new proof for a theorem on chromatic symmetric functions of certain posets.

Contribution

It establishes s-positivity results for interval hypergraphs and related structures, advancing understanding of chromatic functions in combinatorics.

Findings

Proves s-positivity of interval hypergraph chromatic functions

Confirms Taylor's conjecture on s-positivity

Provides a new proof of Gasharov's theorem

Abstract

We prove the s-positivity of the chromatic functions of interval hypergraphs and a conjecture of Taylor~\cite{Taylor15} as a consequence. We also give a new proof of Gasharov's theorem on the s-positivity of the chromatic symmetric functions of $(3+1)$-free posets.