{"paper":{"title":"Zero sum partition into sets of the same order and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sylwia Cichacz","submitted_at":"2017-02-25T09:09:24Z","abstract_excerpt":"We will say that an Abelian group $\\Gamma$ of order $n$ has the $m$-\\emph{zero-sum-partition property} ($m$-\\textit{ZSP-property}) if $m$ divides $n$, $m\\geq 2$ and there is a partition of $\\Gamma$ into pairwise disjoint subsets $A_1, A_2,\\ldots , A_t$, such that $|A_i| = m$ and $\\sum_{a\\in A_i}a = g_0$ for $1 \\leq i \\leq t$, where $g_0$ is the identity element of $\\Gamma$.\n  In this paper we study the $m$-ZSP property of $\\Gamma$. We show that $\\Gamma$ has $m$-ZSP if and only if $|\\Gamma|$ is odd or $m\\geq 3$ and $\\Gamma$ has more than one involution. We will apply the results to the study of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07859","kind":"arxiv","version":1},"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"}