{"paper":{"title":"Coefficients of Sylvester's Denumerant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Brandon Dutra, Jes\\'us De Loera, Matthias K\\\"oppe, Mich\\`ele Vergne, Nicole Berline, Velleda Baldoni","submitted_at":"2013-12-26T20:37:51Z","abstract_excerpt":"For a given sequence $\\mathbf{\\alpha} = [\\alpha_1,\\alpha_2,\\dots,\\alpha_{N+1}]$ of $N+1$ positive integers, we consider the combinatorial function $E(\\mathbf{\\alpha})(t)$ that counts the nonnegative integer solutions of the equation $\\alpha_1x_1+\\alpha_2 x_2+\\cdots+\\alpha_{N} x_{N}+\\alpha_{N+1}x_{N+1}=t$, where the right-hand side $t$ is a varying nonnegative integer. It is well-known that $E(\\mathbf{\\alpha})(t)$ is a quasi-polynomial function in the variable $t$ of degree $N$. In combinatorial number theory this function is known as Sylvester's denumerant.\n  Our main result is a new algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7147","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"}