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A polytope related to empirical distributions, plane trees, parking functions, and the associahedron

Jim Pitman·Richard Stanley
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Abstract

We define an n-dimensional polytope Pi_n(x), depending on parameters x_i>0, whose combinatorial properties are closely connected with empirical distributions, plane trees, plane partitions, parking functions, and the associahedron. In particular, we give explicit formulas for the volume of Pi_n(x) and, when the x_i's are integers, the number of integer points in Pi_n(x). We give two polyhedral decompositions of Pi_n(x), one related to order cones of posets and the other to the associahedron.

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Jim Pitman, Richard Stanley. 1999-08-06. A polytope related to empirical distributions, plane trees, parking functions, and the associahedron. https://arxiv.org/abs/math/9908029

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