{"paper":{"title":"A geometrical characterization of proportionally modular affine semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"A. S\\'anchez-R.-Navarro, A. Vigneron-Tenorio, J. D. D\\'iaz-Ram\\'irez, J. I. Garc\\'ia-Garc\\'ia","submitted_at":"2019-06-04T16:59:46Z","abstract_excerpt":"A proportionally modular affine semigroup is the set of nonnegative integer solutions of a modular Diophantine inequality $f_1x_1+\\cdots +f_nx_n \\mod b \\le g_1x_1+\\cdots +g_nx_n$ where $g_1,\\dots,g_n,$ $f_1,\\ldots ,f_n\\in \\mathbb{Z}$ and $b\\in\\mathbb{N}$. In this work, a geometrical characterization of these semigroups is given. Moreover, some algorithms to check if a semigroup $S$ in $\\mathbb{N}^n$, with $\\mathbb{N}^n\\setminus S$ a finite set, is a proportionally modular affine semigroup are provided by means of that geometrical approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01585","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"}