Colored partitions and a generalization of the braid arrangement
type: Item
instance of: scholarly article
title: Colored partitions and a generalization of the braid arrangement
zbMATH Open document ID: 0883.52010
author: Volkmar Welker
published in: The Electronic Journal of Combinatorics
publication date: 1998-02-12T00:00:00Z
full work available at URL: https://eudml.org/doc/119201
full work available at URL: v4i1r4.html
review text: Summary: We study the topology and combinatorics of an arrangement of hyperplanes in \(\mathbb{C}^n\) that generalizes the classical braid arrangement. The arrangement plays an important role in the work of V. V. Schechtman and A. N. Varchenko on Lie algebra homology, where it appears in a generic fiber of a projection of the braid arrangement. The study of the intersection lattice of the arrangement leads to the definition of lattices of colored partitions. A detailed combinatorial analysis then provides algebro-geometric and topological properties of the complement of the arrangement. Using results on the character of \(S_n\) on the cohomology of these arrangements we are able to deduce the rational cohomology of certain spaces of polynomials in the complement of the standard discriminant that have no root in the first \(s\) integers.
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 05E25
Mathematics Subject Classification ID: 17B55
zbMATH DE Number: 1117989
zbMATH Keywords: arrangement of hyperplanes
zbMATH Keywords: braid arrangement
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1117989