Combinatorial polar orderings and recursively orderable arrangements

Delucchi, Emanuele and Settepanella, Simona (2010) Combinatorial polar orderings and recursively orderable arrangements. Advances in Applied Mathematics, 44 (2). pp. 124-144. ISSN 01968858

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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 recursively order- able 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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