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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>>