A geometric interpretation of Stanley's monotonicity theorem

TL;DR

This paper offers a novel geometric proof of Stanley's monotonicity theorem for lattice polytopes by interpreting δ-polynomials through orbifold Chow rings, providing new insights into their structure.

Contribution

It introduces a geometric approach to prove Stanley's monotonicity theorem using orbifold Chow rings, expanding the theoretical understanding of lattice polytopes.

Findings

New geometric proof of Stanley's monotonicity theorem

Interpretation of δ-polynomials via orbifold Chow rings

Enhanced understanding of lattice polytope structure

Abstract

We present a new geometric proof of Stanley's monotonicity theorem for lattice polytopes, using an interpretation of $\delta$-polynomials of lattice polytopes in terms of orbifold Chow rings.