2018/11/26 by Lorenzo Venturello, Venturello, Lorenzo
Computer Science · Mathematics · #05E45 #52B05 #57Q15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1811.10271
openalex publication_date 2018/11/26 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28
A d-dimensional simplicial complex is balanced if the underlying graph is\n(d+1)-colorable. We present an implementation of cross-flips, a set of local\nmoves introduced by Izmestiev, Klee and Novik which connect any two\nPL-homeomorphic balanced combinatorial manifolds. As a result we exhibit a\nvertex minimal balanced triangulation of the real projective plane, of the\ndunce hat and of the real projective space, as well as several balanced\ntriangulations of surfaces and 3-manifolds on few vertices. In particular we\nconstruct small balanced triangulations of the 3-sphere that are non-shellable\nand shellable but not vertex decomposable.\n