{"paper":{"title":"On the number of fully weighted zero-sum subsequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ab\\'ilio Lemos, Allan O. Moura, Anderson T. Silva, B. K. Moriya","submitted_at":"2018-11-09T13:24:00Z","abstract_excerpt":"Let $G$ be a finite additive abelian group with exponent $n$ and $S=g_{1}\\cdots g_{t}$ be a sequence of elements in $G$. For any element $g$ of $G$ and $A\\subseteq\\{1,2,\\ldots,n-1\\}$, let $N_{A,g}(S)$ denote the number of subsequences $T=\\prod_{i\\in I}g_{i}$ of $S$ such that $\\sum_{i\\in I}a_{i}g_{i}=g$ , where $I\\subseteq\\left\\{ 1,\\ldots,t\\right\\} $ and $a_{i}\\in A$. In this paper, we prove that $N_{A,0}(S)\\geq2^{|S|-D_{A}(G)+1}$, when $A=\\left\\{ 1,\\ldots,n-1\\right\\} $, where $D_{A}(G)$ is the smallest positive integer $l$, such that every sequence $S$ over $G$ of length at least $l$ has nonem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03890","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"}