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arXiv · 0711.1517

Combinatorial polar orderings and recursively orderable arrangements

Emanuele Delucchi·Simona Settepanella
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Abstract

Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal complex is particularly easy, called {\em recursively orderable} arrangements, can therefore be combinatorially defined. We initiate the study of this class, giving a complete characterization in dimension 2 and proving that every supersolvable complexified arrangement is recursively orderable.

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Emanuele Delucchi, Simona Settepanella. 2007-11-09. Combinatorial polar orderings and recursively orderable arrangements. https://doi.org/10.1016/j.aam.2008.11.005

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