{"paper":{"title":"On the Ubiquity and Utility of Cyclic Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Labbate, M. Abreu, M. J. Funk, V. Napolitano","submitted_at":"2011-11-14T16:18:34Z","abstract_excerpt":"Let $k,l,m,n$, and $\\mu$ be positive integers. A $\\mathbb{Z}_\\mu$--{\\it scheme of valency} $(k,l)$ and {\\it order} $(m,n)$ is a $m \\times n$ array $(S_{ij})$ of subsets $S_{ij} \\subseteq \\mathbb{Z}_\\mu$ such that for each row and column one has $\\sum_{j=1}^n |S_{ij}| = k $ and $\\sum_{i=1}^m |S_{ij}| = l$, respectively. Any such scheme is an algebraic equivalent of a $(k,l)$-semi-regular bipartite voltage graph with $n$ and $m$ vertices in the bipartition sets and voltages coming from the cyclic group $\\mathbb{Z}_\\mu$. We are interested in the subclass of $\\mathbb{Z}_\\mu$--schemes that are char"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3265","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"}