• Corpus ID: 237940075

# Projections and angle sums of permutohedra

@inproceedings{Godland2020ProjectionsAA,
title={Projections and angle sums of permutohedra},
author={Thomas Godland and Zakhar Kabluchko},
year={2020}
}
• Published 9 September 2020
• Mathematics
Let (x1, . . . , xn) ∈ R. Permutohedra of types A and B are convex polytopes in R defined by P n = conv{(xσ(1), . . . , xσ(n)) : σ ∈ Sym(n)} and P n = conv{(ε1xσ(1), . . . , εnxσ(n)) : (ε1, . . . , εn) ∈ {±1} n , σ ∈ Sym(n)}, where Sym(n) denotes the group of permutations of the set {1, . . . , n}. We derive a closed formula for the number of j-faces of GP n and GP B n for a linear map G : R n → R satisfying some minor general position assumptions. In particular, we will show that the face…

## References

SHOWING 1-10 OF 29 REFERENCES
A multidimensional analogue of the arcsine law for the number of positive terms in a random walk
• Mathematics
Bernoulli
• 2019
Consider a random walk $S_i= \xi_1+\ldots+\xi_i$, $i\in\mathbb N$, whose increments $\xi_1,\xi_2,\ldots$ are independent identically distributed random vectors on $\mathbb R^d$ such that $\xi_1$ has
Generalized angle vectors, geometric lattices, and flag-angles
• 2018
Intrinsic Volumes of Polyhedral Cones: A Combinatorial Perspective
• Mathematics
Discret. Comput. Geom.
• 2017
This article provides a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones and direct derivations of the general Steiner formula, the conic analogues of the Brianchon–Gram–Euler and the Gauss–Bonnet relations, and the principal kinematic formula are given.
Arrangements Of Hyperplanes
The arrangements of hyperplanes is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Random Conical Tessellations
• Mathematics
Discret. Comput. Geom.
• 2016
The complete covariance structure of the random vector whose components are the k-face contents of the induced spherical random polytopes is determined, which can be considered as a spherical counterpart of a classical result due to Roger Miles.
Convex hulls of random walks, hyperplane arrangements, and Weyl chambers
• Mathematics
• 2015
AbstractWe give an explicit formula for the probability that the convex hull of an n-step random walk in $${\mathbb{R}^d}$$Rd does not contain the origin, under the assumption that the distribution
Living on the edge: phase transitions in convex programs with random data
• Computer Science
• 2013
This paper provides the first rigorous analysis that explains why phase transitions are ubiquitous in random convex optimization problems and introduces a summary parameter, called the statistical dimension, that canonically extends the dimension of a linear subspace to the class of convex cones.
Projection Volumes of Hyperplane Arrangements
• Mathematics
Discret. Comput. Geom.
• 2011
We prove that for any finite real hyperplane arrangement the average projection volumes of the maximal cones are given by the coefficients of the characteristic polynomial of the arrangement. This
Counting the Faces of Randomly-Projected Hypercubes and Orthants, with Applications
• Mathematics
Discret. Comput. Geom.
• 2010
AbstractLet A be an n×N real-valued matrix with n<N; we count the number of k-faces fk(AQ) when Q is either the standard N-dimensional hypercube IN or else the positive orthant ℝ+N. To state results
Enumerative combinatorics
This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.