A lower bound for the Wilf density, deduced from a result of Zhai

2021/07/14 by Hellus, Michael, Rechenauer, Anton, Waldi, Rolf
#11D07 (Primary) 20M14 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2107.06752

Abstract

Let S≠\mathbb N be a numerical semigroup with Frobenius number f, genus g and embedding dimension e. In 1978 Wilf asked the question, whether (f+1-g)/(f+1)≥\frac1e. As is well known, this holds in the cases e=2 and e=3. From Zhai's results in [5] we derive (f+1-g)/(f+1)≥\frac2e²-e+2 for e≥4 .

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