{"paper":{"title":"An Extreme Family of Generalized Frobenius Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Curtis Kifer, Matthias Beck","submitted_at":"2010-05-15T18:19:51Z","abstract_excerpt":"We study a generalization of the \\emph{Frobenius problem}: given $k$ positive relatively prime integers, what is the largest integer $g_0$ that cannot be represented as a nonnegative integral linear combination of these parameters? More generally, what is the largest integer $g_s$ that has exactly $s$ such representations? We illustrate a family of parameters, based on a recent paper by Tripathi, whose generalized Frobenius numbers $g_0, \\ g_1, \\ g_2, ...$ exhibit unnatural jumps; namely, $g_0, \\ g_1, \\ g_k, \\ g_{\\binom{k+1}{k-1}}, \\ g_{\\binom{k+2}{k-1}}, ...$ form an arithmetic progression, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2692","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"}