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• W2017408364 abstract "The volume of the n -dimensional polytope Π n (x):= {y ∈ R n : y i ≥ 0 and y 1 + · · · + y i ≤ x 1 + · · ·+ x i for all 1 ≤ i ≤ n } for arbitrary x:=(x 1 , . . ., x n ) with x i >0 for all i defines a polynomial in variables x i which admits a number of interpretations, in terms of empirical distributions, plane partitions, and parking functions. We interpret the terms of this polynomial as the volumes of chambers in two different polytopal subdivisions of Π n (x) . The first of these subdivisions generalizes to a class of polytopes called sections of order cones. In the second subdivision the chambers are indexed in a natural way by rooted binary trees with n+1 vertices, and the configuration of these chambers provides a representation of another polytope with many applications, the associahedron ." @default.
• W2017408364 created "2016-06-24" @default.
• W2017408364 creator A5013085647 @default.
• W2017408364 creator A5079674634 @default.
• W2017408364 date "2002-01-01" @default.
• W2017408364 modified "2023-10-16" @default.
• W2017408364 title "A Polytope Related to Empirical Distributions, Plane Trees, Parking Functions, and the Associahedron" @default.
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• W2017408364 doi "https://doi.org/10.1007/s00454-002-2776-6" @default.
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