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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*(*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}).

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

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