{"paper":{"title":"Gr{\\\"o}bner basis. a \"pseudo-polynomial\" algorithm for computing the Frobenius number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Dung Nguyen Thi, Marcel Morales","submitted_at":"2015-10-07T14:53:33Z","abstract_excerpt":"Let consider $n$ natural numbers    $a\\_1  ,\\ldots ,  a\\_{n}  $. Let $S$ be the numerical semigroup generated by $a\\_1  ,\\ldots ,  a\\_{n}  $. Set $A=K[t^{a\\_1}, \\ldots , t^{a\\_n}]=K[{x\\_1}, \\ldots , {x\\_n}]/I$. The aim of this paper is:  \\begin{enumerate}\\item Give an effective  pseudo-polynomial algorithm on $a\\_1$,  which computes The Ap{\\'e}ry set and the Frobenius number of $S$. As a consequence it also solves in pseudo-polynomial time the  integer knapsack problem : given a natural integer b, b belongs to $S$?\\item The \\gbb of $I$ for the reverse lexicographic order to $x\\_n,\\ldots ,x\\_1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01973","kind":"arxiv","version":2},"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"}