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arXiv · 1203.1296

On the number of regions and multiplicities of vertices in plane arrangements

Igor Shnurnikov
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Abstract

For an arrangement of $n$ pseudolines in the real projective plane let us denote by $t_i$ the number of vertices incident to $i$ lines. We obtain a linear on $t_i$ inequality similar to the Hirzebruch one, but with an elementary proof. We present an algorithm for producing lower bounds of the number of regions basing on linear on $t_i$ inequalities like the above-mentioned. Lower bounds arise in connection with Martinov theorem on the set of all possible numbers of regions and we show how the new bounds may be applied in it.

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Igor Shnurnikov. 2012-03-06. On the number of regions and multiplicities of vertices in plane arrangements. https://arxiv.org/abs/1203.1296

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