A polytope related to empirical distributions, plane trees, parking functions, and the associahedron
Combinatorics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/9908029,
title = {A polytope related to empirical distributions, plane trees, parking functions, and the associahedron},
author = {Jim Pitman and Richard Stanley},
journal= {arXiv preprint arXiv:math/9908029},
year = {2007}
}
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41 pages