{"paper":{"title":"More on additive triples of bijections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"math.CO","authors_text":"Sean Eberhard","submitted_at":"2017-04-08T00:18:38Z","abstract_excerpt":"We study additive properties of the set $S$ of bijections (or permutations) $\\{1,\\dots,n\\}\\to G$, thought of as a subset of $G^n$, where $G$ is an arbitrary abelian group of order $n$. Our main result is an asymptotic for the number of solutions to $\\pi_1 + \\pi_2 + \\pi_3 = f$ with $\\pi_1,\\pi_2,\\pi_3\\in S$, where $f:\\{1,\\dots,n\\}\\to G$ is an arbitary function satisfying $\\sum_{i=1}^n f(i) = \\sum G$. This extends recent work of Manners, Mrazovi\\'c, and the author. Using the same method we also prove a less interesting asymptotic for solutions to $\\pi_1 + \\pi_2 + \\pi_3 + \\pi_4 = f$, and we also s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02407","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"}