{"paper":{"title":"Modified Erd\\H{o}s-Ginzburg-Ziv Constants for $(\\mathbb{Z}/n\\mathbb{Z})^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Trajan Hammonds","submitted_at":"2019-07-25T21:12:21Z","abstract_excerpt":"For an abelian group $G$ and an integer $t > 0$, the modified Erd\\H{o}s-Ginzburg-Ziv constant $s'_t(G)$ is the smallest integer $\\ell$ such that any zero-sum sequence of length at least $\\ell$ with elements in $G$ contains a zero-sum subsequence (not necessarily consecutive) of length $t$. We compute bounds for $s'_{t}(G)$ for $G = \\left(\\mathbb{Z}/n\\mathbb{Z}\\right)^2$ and $G = \\left(\\mathbb{Z}/n_1\\mathbb{Z} \\times \\mathbb{Z}/n_2\\mathbb{Z}\\right)$. We also compute bounds for $G = \\left(\\mathbb{Z}/p\\mathbb{Z}\\right)^d$ where the subsequence can be any length in $\\{p, \\dots, (d-1)p\\}$. Lastly, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11236","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"}