{"paper":{"title":"On proportionally modular numerical semigroups that are generated by arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Amitabha Tripathi, Edgar Federico Elizeche","submitted_at":"2020-11-03T07:35:23Z","abstract_excerpt":"A numerical semigroup is a submonoid of ${\\mathbb Z}_{\\ge 0}$ whose complement in ${\\mathbb Z}_{\\ge 0}$ is finite. For any set of positive integers $a,b,c$, the numerical semigroup $S(a,b,c)$ formed by the set of solutions of the inequality $ax \\bmod{b} \\le cx$ is said to be proportionally modular. For any interval $[\\alpha,\\beta]$, $S\\big([\\alpha,\\beta]\\big)$ is the submonoid of ${\\mathbb Z}_{\\ge 0}$ obtained by intersecting the submonoid of ${\\mathbb Q}_{\\ge 0}$ generated by $[\\alpha,\\beta]$ with ${\\mathbb Z}_{\\ge 0}$.\n  For the numerical semigroup $S$ generated by a given arithmetic progres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.01527","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.01527/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}