{"paper":{"title":"On a question of Sidorenko","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Cherkashin, F. Petrov, V. Sokolov","submitted_at":"2018-12-20T15:18:33Z","abstract_excerpt":"For a positive integer $n>1$ denote by $\\omega(n)$ the maximal possible number $k$ of different functions $f_1,\\dots,f_k:\\mathbb{Z}/n\\mathbb{Z}\\mapsto \\mathbb{Z}/n\\mathbb{Z}$ such that each function $f_i-f_j,i<j$, is bijective. Recently A. Sidorenko conjectured that $\\omega(n)$ equals to the minimal prime divisor of $n$. We disprove it for $n=15,21,27$ by several counterexamples found by computer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00440","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"}