Séminaire Lotharingien de Combinatoire, 93B.136 (2025), 12 pp.
Alin Bostan, Frédéric Chyzak, Bérénice Delcroix-Oger, Guillaume Laplante-Anfossi, Vincent Pilaud and Kurt Stoeckl
Diagonals of Permutahedra and Associahedra
Abstract.
We present enumeration formulas for the faces of cellular diagonals of the permutahedra and associahedra. For the former, we use Zaslavsky's theory to count the faces of the hyperplane arrangement obtained as the union of ℓ generically translated copies of the braid arrangement. This yields in particular nice formulas for the number of regions and bounded regions in terms of exponentials of generating functions of Fuss-Catalan numbers. For the latter, we use analytic or bijective methods to enumerate Tamari intervals weighted by certain binomial coefficients, leading to a surprisingly simple product formula.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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