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A new Twitter bot helps track wildfires

来源于:MIT Technology
The active bijection for oriented matroids (and real hyperplane arrangements, and graphs, as particular cases) is introduced and investigated by the authors in a series of papers. Given any oriented matroid defined on a linearly ordered ground set, we exhibit one particularit\'e of its bases, which we call its active basis, with remarkable properties. It preserves activities (for oriented matroids in the sense of Las Vergnas, for matroid bases in the sense of Tutte), as well as some active partitions of the ground set associated with oriented matroids and matroid bases. It yields a canonical bijection between classes of reorientations and bases [...]. It also yields a refined bijection between all reorientations and subsets of the ground set. Those bijections are related to various Tutte polynomial expressions [...]. They contain various noticeable bijections involving orientations/signatures/reorientations and spanning trees/simplices/bases of a graph/real hyperplane arrangement/orien 查看全文>>