http://imrn.oxfordjournals.org International Mathematics Research Notices - RSS feed of current issue 1687-0247 2008 International Mathematics Research Notices 1073-7928 http://imrn.oxfordjournals.org/cgi/content/short/2008/rnm167/rnm167?rss=1 Motivated by the work of Salvetti and Settepanella [24, Combinatorial Morse theory and minimality of hyperplane arrangements, Remark 4.5], we give a purely combinatorial description of a class of discrete Morse functions having a minimal number of critical cells for the Salvetti complex of any linear arrangement. We start by studying certain total orderings of the cells of shellable regular CW-complexes, and use them to construct maximum acyclic matchings of the given complex. We apply this technique to the classical zonotope shellings. A new combinatorial stratification of the Salvetti complex allows us to paste such matchings and describe a class of maximum acyclic matchings of the whole complex. The construction can be done, so that the critical cells can be constructed from the chambers via the nbc sets. The results hold for abstract oriented matroids.

]]> 2008-02-08 info:doi/10.1093/imrn/rnm167 Oxford University Press rnm167 2008 39 2008-02-08 rnm167 Research Articles