Simple Euclidean arrangements with one (>=5)-gon

Details Simple Euclidean arrangements with one (>=5)-gon Simple Euclidean arrangements with one (>=5)-gon

2010-08-26

arxiv.org/abs/1008.4598v1

Mathematics

Combinatorics

17 pages, 15 figures

Scientific paper

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.

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