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The generalized Pitman-Stanley polytope
Algebra & Discrete Mathematics| Speaker: | Annie Raymond, U. Mass. Amherst |
| Location: | 1147 MSB |
| Start time: | Tue, Apr 8 2025, 2:10PM |
The eponymous Pitman-Stanley polytope introduced in 1999 is related to plane partitions of skew shape with entries 0 and 1. It has been well studied because of its connections to probability, parking functions, generalized permutahedra, and flow polytopes. We consider a generalization of this polytope related to plane partitions with entries 0, 1, ... , m. We show that this polytope can also be realized as a flow polytope of a grid graph. We give multiple characterizations of its vertices in terms of plane partitions of skew shape and integer flows. We also study formulas for the volume as well as for the number of lattice points and vertices of this polytope. This is joint work with William Dugan, Maura Hegarty and Alejandro Morales.