{"paper":{"title":"Minimal genus of a multiple and Frobenius number of a quotient of a numerical semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.GR","authors_text":"Francesco Strazzanti","submitted_at":"2015-12-02T10:34:56Z","abstract_excerpt":"Given two numerical semigroups $S$ and $T$ and a positive integer $d$, $S$ is said to be one over $d$ of $T$ if $S=\\{s \\in \\mathbb{N} \\ | \\ ds \\in T \\}$ and in this case $T$ is called a $d$-fold of $S$. We prove that the minimal genus of the $d$-folds of $S$ is $g + \\lceil \\frac{(d-1)f}{2} \\rceil$, where $g$ and $f$ denote the genus and the Frobenius number of $S$. The case $d=2$ is a problem proposed by Robles-P\\'erez, Rosales, and Vasco. Furthermore, we find the minimal genus of the symmetric doubles of $S$ and study the particular case when $S$ is almost symmetric. Finally, we study the Fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00638","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"}