2019/10/15 by Matthew Dyer, Weijia Wang, Dyer, Matthew +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.1910.06665
openalex publication_date 2019/10/15 · openalex created_date 2019/10/25 · openalex updated_date 2026/07/28
This paper shows that simplicial oriented geometries can be characterized as groupoids with root systems having certain favorable properties, as conjectured by the first author. The proof first translates Handa's characterization of oriented matroids, as acycloids which remain acycloids under iterated elementary contractions, into the language of groupoids with root systems, then establishes favorable lattice theoretic properties of a generalization of a construction which Brink and Howlett used in their study of normalizers of parabolic subgroups of Coxeter groups and uses Björner-Edelman-Ziegler's lattice theoretic characterization of simplicial oriented geometries amongst oriented geometries.