{"paper":{"title":"On the Index of Sequences over Cyclic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Chris Plyley, Guoqing Wang, Jiangtao Peng, Weidong Gao, Yuanlin Li","submitted_at":"2009-09-14T02:18:06Z","abstract_excerpt":"Let $G$ be a finite cyclic group of order $n \\ge 2$. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\\cdot ... \\cdot (n_lg)$ where $g\\in G$ and $n_1,..., n_l \\in [1,\\ord(g)]$, and the index $\\ind (S)$ of $S$ is defined as the minimum of $(n_1+ ... + n_l)/\\ord (g)$ over all $g \\in G$ with $\\ord (g) = n$. In this paper we prove that a sequence $S$ over $G$ of length $|S| = n$ having an element with multiplicity at least $\\frac{n}{2}$ has a subsequence $T$ with $\\ind (T) = 1$, and if the group order $n$ is a prime, then the assumption on the multiplicity can be relaxed to $\\frac{n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2461","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"}