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Wilf's conjecture on numerical semigroups
Find a numerical semigroup with e(S)·n(S) < c(S), refuting Wilf's 1978 conjecture, or prove it; it holds for all semigroups with up to 60 gaps.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "number-theory", |
| 5 | "algebra", |
| 6 | "combinatorics" |
| 7 | ], |
| 8 | "type": "construction", |
| 9 | "also": [ |
| 10 | "proof" |
| 11 | ], |
| 12 | "source": { |
| 13 | "key": "frontiermath-open", |
| 14 | "name": "FrontierMath: Open Problems", |
| 15 | "url": "https://epoch.ai/frontiermath/open-problems/numerical-semigroups", |
| 16 | "id": "numerical-semigroups", |
| 17 | "curator": "Epoch AI", |
| 18 | "poser": "Herbert S. Wilf", |
| 19 | "status": "unsolved", |
| 20 | "as_of": "2026-10-20", |
| 21 | "catalog": "0521c19bbd38" |
| 22 | }, |
| 23 | "review": true, |
| 24 | "approval": "first-time" |
| 25 | } |