{"paper":{"title":"The existence of square non-integer Heffter arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Diane Donovan, Jeff Dinitz, Nicholas J. Cavenagh, Sule Yaz{\\i}c{\\i}","submitted_at":"2018-08-08T00:07:04Z","abstract_excerpt":"A Heffter array $H(n;k)$ is an $n\\times n$ matrix such that each row and column contains $k$ filled cells, each row and column sum is divisible by $2nk+1$ and either $x$ or $-x$ appears in the array for each integer $1\\leq x\\leq nk$. Heffter arrays are useful for embedding the graph $K_{2nk+1}$ on an orientable surface. An integer Heffter array is one in which each row and column sum is $0$. Necessary and sufficient conditions (on $n$ and $k$) for the existence of an integer Heffter array $H(n;k)$ were verified by Archdeacon, Dinitz, Donovan and Yaz\\i c\\i \\ (2015) and Dinitz and Wanless (2017)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02588","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"}