Séminaire Lotharingien de Combinatoire, 93B.11 (2025), 12 pp.
Fu Liu and Warut Thawinrak
Faces of Parking Function Polytopes
Abstract.
We extended the notion of parking function polytopes and explored their normal fans, face posets, and h-polynomials. To capture their combinatorial properties, we introduced generalizations of ordered set partitions, which we refer to as binary partitions and skewed binary paritions. Using properties of preorder cones, we developed tools to characterize the family of skewed binary partitions that bijectively corresponds to the normal fan of a parking function polytope. Additionally, we gave a formula for the h-polynomials of simple parking function polytopes in terms of generalized Eulerian polynomials.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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