{"paper":{"title":"The numerical duplication of a numerical semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Francesco Strazzanti, Marco D'Anna","submitted_at":"2012-11-15T18:41:10Z","abstract_excerpt":"In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup $S$ and a semigroup ideal $E\\subseteq S$, produces a new numerical semigroup, denoted by $S\\Join^b\\E$ (where $b$ is any odd integer belonging to $S$), such that $S=(S\\Join^b\\E)/2$. In particular, we characterize the ideals $E$ such that $S\\Join^bE$ is almost symmetric and we determine its type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3693","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"}