Simple Euclidean arrangements with one (>=5)-gon
Combinatorics
2010-08-30 v1
Abstract
Let L be a simple Euclidean arrangement of n pseudolines. It is shown that if L has exactly one (>=5)=gon P, and k is the number of edges of P that are adjacent to an unbounded cell of the subarrangement of L induced by the pseudolines in P, then L has exactly n-k triangles and k+n(n-5)/2 quadrilaterals. We also prove that if each pseudoline of L is adjacent to P then L is stretchable.
Cite
@article{arxiv.1008.4598,
title = {Simple Euclidean arrangements with one (>=5)-gon},
author = {Jesus Leaños and Mbe Koua Christophe Ndjatchi and Luis Manuel Rivera-Martinez},
journal= {arXiv preprint arXiv:1008.4598},
year = {2010}
}
Comments
17 pages, 15 figures