Weighted quasisymmetric enumerator for generalized permutohedra

TL;DR

This paper introduces a weighted quasisymmetric enumerator function for generalized permutohedra that refines existing functions and encodes face number information, with a focus on nestohedra and matroid base polytopes.

Contribution

It presents a new weighted quasisymmetric enumerator function that extends previous functions and captures face number data for generalized permutohedra.

Findings

Refinement of Billera, Jia, and Reiner's quasisymmetric function

Inclusion of face number information of generalized permutohedra

Systematic analysis of nestohedra and matroid base polytopes

Abstract

We introduce a weighted quasisymmetric enumerator function associated to generalized permutohedra. It refines the Billera, Jia and Reiner quasisymmetric function which also includes the Stanley chromatic symmetric function. Beside that it carries information of face numbers of generalized permutohedra. We consider more systematically the cases of nestohedra and matroid base polytopes.