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To an extended permutohedron we associate the weighted integer pointsenumerator, whose principal specialization is the $f$-polynomial. In the caseof poset cones it refines Gessel's $\mathsf{P}$-partitions enumerator. We showthat this enumerator is a quasisymmetric function obtained by universalmorphism from the Hopf algebra of posets.

Weighted $\mathsf{P}-$partitions enumerator