The active bijection between regions and simplices in supersolvable arrangements of hyperplanes

zbMath1188.52025MaRDI QIDQ2380207

Emeric Gioan, Michel Las Vergnas

Publication date: 26 March 2010

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/228188

zbMATH Keywords

activitypermutationbijectionoriented matroidbasismatroidTutte polynomialno broken circuithyperplane arrangementCoxeter arrangementsupersolvableincreasing treereorientationbraid arrangementregionhyperoctahedral arrangement

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Combinatorial aspects of matroids and geometric lattices (05B35) Varieties of lattices (06B20) Oriented matroids in discrete geometry (52C40)

Related Items (7)

Fully Optimal Bases and the Active Bijection in Graphs, Hyperplane Arrangements, and Oriented Matroids ⋮ Computing the fully optimal spanning tree of an ordered bipolar directed graph ⋮ Bijections between affine hyperplane arrangements and valued graphs ⋮ The active bijection for graphs ⋮ The active bijection in graphs, hyperplane arrangements, and oriented matroids, 1: the fully optimal basis of a bounded region ⋮ Activity preserving bijections between spanning trees and orientations in graphs ⋮ A Linear Programming Construction of Fully Optimal Bases in Graphs and Hyperplane Arrangements

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