{"paper":{"title":"Erd\\H{o}s-Szekeres theorem for cyclic permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Eva Czabarka, Zhiyu Wang","submitted_at":"2018-04-07T17:14:45Z","abstract_excerpt":"We provide a cyclic permutation analogue of the Erd\\H os-Szekeres theorem. In particular, we show that every cyclic permutation of length $(k-1)(\\ell-1)+2$ has either an increasing cyclic sub-permutation of length $k+1$ or a decreasing cyclic sub-permutation of length $\\ell+1$, and show that the result is tight. We also characterize all maximum-length cyclic permutations that do not have an increasing cyclic sub-permutation of length $k+1$ or a decreasing cyclic sub-permutation of length $\\ell+1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02578","kind":"arxiv","version":2},"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"}