Wilf's conjecture

Wilf's conjecture is a hypothesis in number theory concerning numerical semigroups—sets of non-negative integers closed under addition with a finite complement. The conjecture proposes a specific inequality relating three key features of such a semigroup: its multiplicity (smallest non-zero element), its Frobenius number (largest integer not in the set), and the number of gaps (missing integers up to the Frobenius number). Essentially, it suggests a certain balance or relationship among these elements holds universally across all numerical semigroups, guiding mathematicians in understanding their structure.