Deformations of Coxeter hyperplane arrangements and their characteristic polynomials

By Christos A. Athanasiadis. 2000

51 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/e9712146e8a74986280ab4a2c2f5f8b31390a0c6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Drew Armstrong
2. Masahiko Yoshinaga
3. Federico Ardila
4. Christos A. Athanasiadis
5. Victor Reiner
6. Takuro Abe
7. David Bessis
8. Sergey Fomin

In Discrete Mathematics and Combinatorics

1. Drew Armstrong
2. Masahiko Yoshinaga
3. Federico Ardila
4. Christos A. Athanasiadis
5. Takuro Abe
6. Victor Reiner
7. Mario Salvetti
8. David Bessis

In Electrical and Electronic Engineering

1. Masahiko Yoshinaga
2. Federico Ardila
3. Drew Armstrong
4. Christos A. Athanasiadis
5. Takuro Abe

Citations in the corpus

• COMPUTING THE TUTTE POLYNOMIAL OF A HYPERPLANE ARRAGEMENT (2004, background): “x i − x j = a (1) ij ,...,a (k ij) ij for 1 ≤ i < j ≤ n, where the k ij are non-negative integers, and the a(r) ij are real numbers. Such arrangements have been studied extensively by Athanasiadis [6] and Postnikov and Stanley [28]. In this section we study their coboundary polynomials. Theorem 4”
• Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (2006, background): “Let [n]q! = [n]q[n − 1]q · · · [2]q[1]q denote the q-factorial and let [ n k ] q denote the standard q-binomal coefficient [n]q [k]q[n−k]q .”
• Characterization of a free arrangement and conjecture of Edelman and Reiner (2004, background): “And their combinatorics was investigated by many people [Sta], [Ath1], [ER], [He], [PS], [Ath4]. See [ Ath3 ] for a survey.”
• Generalized cluster complexes and Coxeter combinatorics (2005, unknown): “The extended Catalan arrangement CatΦ (see [1, 21]) is the collection of affine hyperplanes Hα,j defined by the equations 〈α, x〉 = j for α ∈ Φ and j = 0, 1, .”
• On a refinement of the generalized Catalan numbers for Weyl groups (2004, background): “Thus CatΦ is a deformation of the Coxeter arrangement AΦ, in the sense of [1, 16], known as an extended Catalan arrangement.”
• Generalized Catalan Numbers, Weyl Groups and Arrangements of Hyperplanes (2004, background): “Thus AΦ is a deformation of the Coxeter hyperplane arrangement AΦ, in the sense of [4, 17], which is invariant under the action of the Weyl group W associated to Φ.”