Results 1 to 10 of about 312,013 (185)
Hyperplane Arrangements in polymake [PDF]
Lecture Notes in Computer Science, 2020 Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm performs significantly better than brute force alternatives, as it requires less convex hulls computations.
Marta Panizzut, Lars Kästner
exaly +6 more sources
Hyperplane Arrangements and Diagonal Harmonics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In 2003, Haglund's bounce statistic gave the first combinatorial interpretation of the q,t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type
Drew Armstrong
doaj +5 more sources
The Varchenko determinant of an oriented matroid [PDF]
Transactions on Combinatorics, 2021 Varchenko introduced in 1993 a distance function on the chambers of a hyperplane arrangement that gave rise to a determinant whose entry in position $(C, D)$ is the distance between the chambers $C$ and $D$, and computed that determinant. In 2017, Aguiar
Hery Randriamaro
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Affine and toric arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We extend the Billera―Ehrenborg―Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements.
Richard Ehrenborg +2 more
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An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs,
Takuro Abe, Koji Nuida, Yasuhide Numata
doaj +1 more source
IET Networks, EarlyView., 2022 Abstract Sensor technology advancements have provided a viable solution to fight COVID and to develop healthcare systems based on Internet of Things (IoTs). In this study, image processing and Artificial Intelligence (AI) are used to improve the IoT framework.
Noor M Allayla +2 more
wiley +1 more source
Bases for modules of differential operators [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 It is well-known that the derivation modules of Coxeter arrangements are free. Holm began to study the freeness of modules of differential operators on hyperplane arrangements. In this paper, we study the cases of the Coxter arrangements of type A, B and
Norihiro Nakashima
doaj +1 more source
Pseudo-Permutations II: Geometry and Representation Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper, we provide the second part of the study of the pseudo-permutations. We first derive a complete analysis of the pseudo-permutations, based on hyperplane arrangements, generalizing the usual way of translating the permutations. We then study
François Boulier +3 more
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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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