Weighted quasisymmetric enumerator for generalized permutohedra
Vladimir Gruji\'c, Marko Pe\v{s}ovi\'c, Tanja Stojadinovi\'c

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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · graph theory and CDMA systems
