{"paper":{"title":"On Numerical Semigroups with Fixed Quotient","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ignacio Ojeda, Jos\\'e Carlos Rosales","submitted_at":"2026-05-14T12:41:07Z","abstract_excerpt":"Let $\\Delta$ be a numerical semigroup and let $d\\ge 2$ be an integer. We study the fiber of the quotient map \\(S\\mapsto S/d\\) over $\\Delta$. We describe its elements as semigroups of the form $\\langle X\\rangle+d\\Delta$, for suitable finite sets $X\\subseteq\\Delta$, and then analyze explicit and computable regions of this fiber. In particular, we introduce a family $\\Delta_d(a)$ of multiples with prescribed quotient and compute its generators, classical invariants, Ap\\'ery sets, and presentations. We also show that this construction preserves Wilf's inequality and controls the depth. Finally, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14775","kind":"arxiv","version":1},"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"}