1Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier, Case Courrier 051, Place Eugene Bataillon, 34095 Montpellier Cedex 05, France.
The electronic journal of combinatorics, Tome 22 (2015) no. 2
J.-P. Roudneff has conjectured that every arrangement of $n\ge 2d+1\ge 5$ (pseudo) hyperplanes in the real projective space $\mathbb{P}^d$ has at most $\sum_{i=0}^{d-2} \binom{n-1}{i}$ cells bounded by each hyperplane. In this note, we show the validity of this conjecture for arrangements arising from Lawrence oriented matroids.
Classification :
52C40, 05C35, 52C35
Mots-clés :
Lawrence oriented matroids, arrangements of hyperplanes
Affiliations des auteurs :
Luis Pedro Montejano
1
;
Jorge Luis Ramírez-Alfonsín
1
1
Université Montpellier 2, Institut de Mathématiques et de Modélisation de Montpellier,
Case Courrier 051, Place Eugene Bataillon, 34095 Montpellier Cedex 05, France.
@article{10_37236_4811,
author = {Luis Pedro Montejano and Jorge Luis Ram{\'\i}rez-Alfons{\'\i}n},
title = {Roudneff's conjecture for {Lawrence} oriented matroids},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/4811},
zbl = {1316.52033},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4811/}
}
TY - JOUR
AU - Luis Pedro Montejano
AU - Jorge Luis Ramírez-Alfonsín
TI - Roudneff's conjecture for Lawrence oriented matroids
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4811/
DO - 10.37236/4811
ID - 10_37236_4811
ER -
%0 Journal Article
%A Luis Pedro Montejano
%A Jorge Luis Ramírez-Alfonsín
%T Roudneff's conjecture for Lawrence oriented matroids
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4811/
%R 10.37236/4811
%F 10_37236_4811
Luis Pedro Montejano; Jorge Luis Ramírez-Alfonsín. Roudneff's conjecture for Lawrence oriented matroids. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4811
