منابع مشابه
Mixed Volumes of Hypersimplices
In this paper we consider mixed volumes of combinations of hypersimplices. These numbers, called “mixed Eulerian numbers”, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan numbers, binomial coefficients, etc. We give a general combinatorial interpretation for mixed Eulerian numbers and prove the above properties combinatorially...
متن کاملRandom Walks and Mixed Volumes of Hypersimplices
Below is a method for relating a mixed volume computation for polytopes sharing many facet directions to a symmetric random walk. The example of permutahedra and particularly hypersimplices is expanded upon.
متن کاملMixed Volumes of Hypersimplices , Root Systems and Shifted
This thesis consists of two parts. In the first part, we start by investigating the classical permutohedra as Minkowski sums of the hypersimplices. Their volumes can be expressed as polynomials whose coefficients the mixed Eulerian numbers are given by the mixed volumes of the hypersimplices. We build upon results of Postnikov and derive various recursive and combinatorial formulas for the mixe...
متن کاملComputing Mixed Discriminants , Mixed Volumes
We construct a probabilistic polynomial time algorithm that computes the mixed discriminant of given n positive definite n × n matrices within a 2O(n) factor. As a corollary, we show that the permanent of an n×n nonnegative matrix and the mixed volume of n ellipsoids inRn can be computed within a 2O(n) factor by probabilistic polynomial time algorithms. Since every convex body can be approximat...
متن کاملBezout Inequality for Mixed Volumes
In this paper we consider the following analog of Bezout inequality for mixed volumes: V (P1, . . . , Pr,∆ )Vn(∆) r−1 ≤ r ∏ i=1 V (Pi,∆ ) for 2 ≤ r ≤ n. We show that the above inequality is true when ∆ is an n -dimensional simplex and P1, . . . , Pr are convex bodies in R . We conjecture that if the above inequality is true for all convex bodies P1, . . . , Pr , then ∆ must be an n -dimensional...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5770