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

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

1999-08-06

arxiv.org/abs/math/9908029v1

Mathematics

Combinatorics

41 pages

Scientific paper

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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