{"paper":{"title":"Variants on a question of Wilf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Anton Rechenauer, Michael Hellus, Rolf Waldi","submitted_at":"2018-04-17T09:56:47Z","abstract_excerpt":"Let $S\\neq\\mathbb N$ be a numerical semigroup generated by $e$ elements. In his paper (A Circle-Of-Lights Algorithm for the \"Money-Changing Problem\", Amer. Math. Monthly 85 (1978), 562--565), H.~S.~Wilf raised the following question: Let $\\Omega$ be the number of positive integers not contained in $S$ and $c-1$ the largest such element. Is it true that the fraction $\\frac\\Omega c$ of omitted numbers is at most $1-\\frac1e$?\n  Let $B\\subseteq\\mathbb N^{e-1}$ be the complement of an artinian $\\mathbb N^{e-1}$-ideal. Following a concept of A.~Zhai (An asymptotic result concerning a question of Wil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06141","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}