Séminaire Lotharingien de Combinatoire, 93B.94 (2025), 12 pp.
William T. Dugan, Maura Hegarty, Alejandro H. Morales and Annie Raymond
Volume and Lattice Points of Generalized Pitman-Stanley Flow Polytopes
Abstract.
The Pitman-Stanley polytope is well-studied and related to plane partitions of skew shape with entries 0 and 1. We study a generalization of this polytope related to plane partitions with entries 0,1,...,m.
%Having previously showed that this polytope is a flow polytope of a grid graph,
We study formulas for the volume and lattice points of this polytope. These formulas have rich combinatorics including connections to standard Young tableaux of rectangular shape. We also give a combinatorial proof for a special case, partially answering a question of Pitman and Stanley.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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