Two Bijections on NBC Subsets

We establish two explicit bijections: from acyclic reorientations of an oriented matroid to no broken circuit (NBC) subsets of its underlying matroid, and from regions of a real hyperplane arrangement to its affine NBC subsets.

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Hauptverfasser: Fu, Houshan, Peng, Baoren, Wang, Suijie, Yang, Jinxing
Format: Artikel
Sprache:eng
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Zusammenfassung:We establish two explicit bijections: from acyclic reorientations of an oriented matroid to no broken circuit (NBC) subsets of its underlying matroid, and from regions of a real hyperplane arrangement to its affine NBC subsets.
DOI:10.48550/arxiv.2408.03719