Improved Upper Bounds on Key Invariants of Erd\H{o}s-R\'enyi Numerical Semigroups

Autor:	Bogart, Tristram, Morales, Santiago
Rok vydání:	2024
Předmět:	Mathematics - Commutative Algebra Mathematics - Combinatorics Mathematics - Number Theory 20M14 06F05 05D40 11P70
Druh dokumentu:	Working Paper
Popis:	De Loera, O'Neill and Wilburne introduced a general model for random numerical semigroups in which each positive integer is chosen independently with some probability p to be a generator, and proved upper and lower bounds on the expected Frobenius number and expected embedding dimensions. We use a range of probabilistic methods to improve the upper bounds to within a polylogarithmic factor of the lower bounds in each case. As one of the tools to do this, we prove that for any prime q, if A is a random subset of the cyclic group Z_q whose size is of order log(q) and k is also of order log(q), then with high probability the k-fold sumset kA is all of Z_q. Comment: 17 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.13767 Zobrazit plný text záznamu View this record from Arxiv