Zeros of the zeta series of a poset and iterated barycentric subdivision

TL;DR

This paper investigates how the zeros of the zeta series of a finite poset behave under repeated barycentric subdivision, exploring potential applications to number theory.

Contribution

It introduces an analysis of the zeros' limiting behavior in posets undergoing barycentric subdivision, a novel approach linking combinatorics and number theory.

Findings

Zeros exhibit specific limiting patterns under subdivision

Potential connections to number theory are suggested

Framework for analyzing poset zeta series zeros

Abstract

We study the limiting behavior of the zeros of the zeta series of a finite poset under iterated barycentric subdivision, and we indicate the possibility of its application to number theory.