Séminaire Lotharingien de Combinatoire, 89B.80 (2023), 12 pp.
William T. Dugan, Maura Hegarty, Alejandro H. Morales and Annie Raymond
Generalized Pitman-Stanley Flow Polytopes
Abstract.
The Pitman-Stanley polytope is well-studied and related to plane partitions with entries 0 and 1. We study a generalization of this polytope related to plane partitions with entries 0,1,...,m. We show that this generalization is realized as a flow polytope of a grid graph. We give multiple characterizations of its vertices and give formulas for the number of vertices and faces. We also study formulas for its number of lattice points and volume.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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