Counting faces of nestohedra

Vladimir Grujić; Tanja Stojadinović

Counting faces of nestohedra

Combinatorics 2017-10-24 v2

Authors: Vladimir Grujić , Tanja Stojadinović

Abstract

A new algebraic formula for the numbers of faces of nestohedra is obtained. The enumerator function $F(P_B)$ of positive lattice points in interiors of maximal cones of the normal fan of the nestohedron $P_B$ associated to a building set $B$ is described as a morphism from the certain combinatorial Hopf algebra of building sets to quasisymmetric functions. We define the $q$ -analog $F_q(P_B)$ and derive its determining recurrence relations. The $f$ -polynomial of the nestohedron $P_B$ appears as the principal specialization of the quasisymmetric function $F_q(P_B)$ .

Keywords

nestohedra face enumeration building sets combinatorial Hopf algebra quasisymmetric functions f-polynomial lattice points

Cite

@article{arxiv.1703.08826,
  title  = {Counting faces of nestohedra},
  author = {Vladimir Grujić and Tanja Stojadinović},
  journal= {arXiv preprint arXiv:1703.08826},
  year   = {2017}
}

Comments

Preprint is merged with arXiv:1704.06715 Face enumeration on matroid base polytopes and redirected to combined version

Counting faces of nestohedra

Abstract

Keywords

Cite

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