Séminaire Lotharingien de Combinatoire, 85B.61 (2021), 12 pp.

José Bastidas

The Polytope Algebra of Generalized Permutahedra

Abstract. We study the polytope algebra of McMullen relative to a fixed zonotope. We endow the corresponding subalgebra with the structure of a module over the Tits algebra of the corresponding hyperplane arrangement. In the case of Coxeter arrangements of type A and B, we find connections with statistics on (signed) permutations and with the Hopf monoid of generalized permutahedra of Aguiar and Ardila.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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