Wilf's conjecture for numerical semigroups with large second generator

Dario Spirito

paper

Wilf's conjecture for numerical semigroups with large second generator

arXiv:1710.09245

Abstract

We study Wilf's conjecture for numerical semigroups $S$ such that the second least generator $a_{2}$ of $S$ satisfies $a_{2} > \frac{c ( S ) + μ ( S )}{3}$ , where $c (S)$ is the conductor and $μ (S)$ the multiplicity of $S$ . In particular, we show that for these semigroups Wilf's conjecture holds when the multiplicity is bounded by a quadratic function of the embedding dimension.