Results 31 to 40 of about 1,232 (194)
Cell Complexities in Hyperplane Arrangements [PDF]
Discrete and Computational Geometry, 2004 The complexity of some cells of an hyperplane arrangement in \(R^d\) is the total number of faces of all dimensions of these cells. The authors show that the complexity of \(m\) distinct cells in an arrangement of \(n\) hyperplanes in dimension \(d\geq 4\) is \(O(m^{1/2}n^{d/2}\log^{(\lfloor d/2\rfloor-2)}n)\).
Boris Aronov, Micha Sharir
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Combinatorial Depth Measures for Hyperplane Arrangements [PDF]
, 2023 Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of data points.
Soberón, Pablo, Schnider, Patrick
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The module of affine descents [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The goal of this paper is to introduce an algebraic structure on the space spanned by affine descent classes of a Weyl group, by analogy and in relation to the structure carried by ordinary descent classes.
Marcelo Aguiar, Kile T. Petersen
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Phylogenetic trees and the tropical geometry of flag varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We will discuss some recent theorems relating the space of weighted phylogenetic trees to the tropical varieties of each flag variety of type A. We will also discuss the tropicalizations of the functions corresponding to semi-standard tableaux, in ...
Christopher Manon
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Branched Polymers and Hyperplane Arrangements [PDF]
Discrete & Computational Geometry, 2013 We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie, and Kenyon and Winkler to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is ...
Postnikov, Alexander, Meszaros, Karola
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On polytopes and generalizations of the KLT relations
Journal of High Energy Physics, 2020 We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT).
Nikhil Kalyanapuram
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Four Variations on Graded Posets [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We explore the enumeration of some natural classes of graded posets, including $(2 + 2)$-avoiding graded posets, $(3 + 1)$-avoiding graded posets, $(2 + 2)$- and $(3 + 1)$-avoiding graded posets, and the set of all graded posets.
Yan X Zhang
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On Minimal Strings Containing the Elements of S_n by Decimation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 The permutations by decimation problem is thought to be applicable to computer graphics, and raises interesting theoretical questions in combinatory theory.We present the results of some theoretical and practical investigation into this problem.We show ...
Robert Erra, Nik Lygeros, Nigel Stewart
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Affine permutations and rational slope parking functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our construction to
Eugene Gorsky +2 more
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Odd Khovanov homology for hyperplane arrangements [PDF]
, 2016 We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincaré polynomial, and Tutte polynomial.
Dancso, Zsuzsanna, Licata, Anthony
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