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Watch a one-hour mathematics lecture exploring the generalized Pitman-Stanley flow polytope, where Alejandro Morales Borrero delves into the evolution and properties of this mathematical structure. Learn about the original polytope introduced by Pitman and Stanley in 1999, its connections to parking functions, lattice path matroids, and flow polytopes, and discover how its lattice points correspond to plane partitions of skew shape. Explore new research on the generalized version, including its realization as a flow polytope of a grid graph, vertex characterizations, and formulas for counting vertices, faces, lattice points, and volume calculations using rectangular Standard Young Tableaux. Understand the latest developments in volume polynomial formulas of flow polytopes through vector partition functions, presented as collaborative research with Maura Hegarty, William Dugan, and Annie Raymond.
