Poset vectors and generalized permutohedra

TL;DR

This paper links the combinatorial structure of posets and subposets to geometric objects called generalized permutohedra, providing a new way to understand integer points related to linear extensions.

Contribution

It introduces a novel geometric interpretation of integer points from linear extensions of posets restricted to subposets using generalized permutohedra.

Findings

Integer points of linear extensions correspond to lattice points of generalized permutohedra

Provides a geometric framework for analyzing poset linear extensions

Establishes a connection between poset theory and polyhedral geometry

Abstract

We show that given a poset P and and a subposet Q, the integer points obtained by restricting linear extensions of P to Q can be explained via integer lattice points of a generalized permutohedron.