A polytope related to empirical distributions, plane trees, parking functions, and the associahedron
Abstract
We define an n-dimensional polytope Pin(x), depending on parameters xi>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 Pin(x) and, when the xi's are integers, the number of integer points in Pin(x). We give two polyhedral decompositions of Pin(x), one related to order cones of posets and the other to the associahedron.
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