Weighted quasisymmetric enumerator for generalized permutohedra

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.

This is a combined and extended version of two preprints arXiv:1704.06715 Face enumeration on matroid base polytopes and arXiv:1703.08826 Counting faces of nestohedra