{"paper":{"title":"Davenport constant for semigroups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang","submitted_at":"2014-09-07T03:08:07Z","abstract_excerpt":"Let $\\mathcal{S}$ be a finite commutative semigroup. The Davenport constant of $\\mathcal{S}$, denoted ${\\rm D}(\\mathcal{S})$, is defined to be the least positive integer $\\ell$ such that every sequence $T$ of elements in $\\mathcal{S}$ of length at least $\\ell$ contains a proper subsequence $T'$ ($T'\\neq T$) with the sum of all terms from $T'$ equaling the sum of all terms from $T$. Let $q>2$ be a prime power, and let $\\F_q[x]$ be the ring of polynomials over the finite field $\\F_q$. Let $R$ be a quotient ring of $\\F_q[x]$ with $0\\neq R\\neq \\F_q[x]$. We prove that $${\\rm D}(\\mathcal{S}_R)={\\rm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2077","kind":"arxiv","version":3},"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"}