2017/10/03 by Jesús A. De Loera, De Loera, Jesus, Christopher O’Neill +3 · 1 citation
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1710.00979
We examine properties of random numerical semigroups under a probabilistic\nmodel inspired by the Erdos-Renyi model for random graphs. We provide a\nthreshold function for cofiniteness, and bound the expected embedding\ndimension, genus, and Frobenius number of random semigroups. Our results\nfollow, surprisingly, from the construction of a very natural shellable\nsimplicial complex whose facets are in bijection with irreducible numerical\nsemigroups of a fixed Frobenius number and whose h-vector determines the\nprobability that a particular element lies in the semigroup.\n