{"paper":{"title":"Erd\\H{o}s-Ginzburg-Ziv theorem for finite commutative semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Guoqing Wang, Sukumar Das Adhikari, Weidong Gao","submitted_at":"2013-09-22T10:52:07Z","abstract_excerpt":"Let $\\mathcal{S}$ be a finite commutative semigroup written additively, and let $\\exp(\\mathcal{S})$ be its exponent which is defined as the least common multiple of all periods of the elements in $\\mathcal{S}$. For every sequence $T$ of elements in $\\mathcal{S}$ (repetition allowed), let $\\sigma(T) \\in \\mathcal{S}$ denote the sum of all terms of $T$. Define the Davenport constant $D(\\mathcal{S})$ of $\\mathcal{S}$ to be the least positive integer $d$ such that every sequence $T$ over $\\mathcal{S}$ of length at least $d$ contains a proper subsequence $T'$ with $\\sigma(T')=\\sigma(T)$, and define "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5588","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"}