We study Wilf’s conjecture for numerical semigroups S such that the second least generator a2 of S satisfies a2 > 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.

中文翻译：

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具有大第二生成元的数值半群的 Wilf 猜想

我们研究了数值半群的 Wilf 猜想小号使得第二小的生成器一种2的小号满足一种2 > C(小号)+μ(小号) 3， 在哪里C(小号)是导体并且μ(小号)的多样性小号. 特别是，我们表明，对于这些半群，当多重性由嵌入维数的二次函数界定时，Wilf 猜想成立。