Séminaire Lotharingien de Combinatoire, 78B.17 (2017), 7 pp.

Vladimir Grujić and Tanja Stojadinović

Counting Faces of Nestohedra

Abstract. A new algebraic formula for the numbers of faces of nestohedra is obtained. The enumerator function F(PB) of positive lattice points in interiors of maximal cones of the normal fan of the nestohedron PB 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 Fq(PB) and derive its determining recurrence relations. The f-polynomial of the nestohedron PB appears as the principal specialization of the quasisymmetric function Fq(PB).

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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