Weighted quasisymmetric enumerator for generalized permutohedra
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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.
Keywords:generalized permutohedron / quasisymmetric function / matroid / matroid base polytope / combinatorial Hopf algebra / f-polynomial
Source:Journal of Algebraic Combinatorics, 2020, 51, 247-272