{"paper":{"title":"Tur\\'an numbers of $4$-uniform tight even cycles minus one edge","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongbin Zhao, Jianfeng Hou, Wanfang Chen, Xizhi Liu, Yixiao Zhang","submitted_at":"2026-06-22T04:10:00Z","abstract_excerpt":"For every integer $k \\ge 1$ and sufficiently large $n$, we show that the extremal construction for the Tur\\'{a}n number of the $4$-uniform tight cycle of length $4k+2$ minus one edge is a complete odd-bipartite $4$-graph. In particular, since $C_{6}^{4-}$ contains the $4$-uniform expanded triangle as a subgraph, our result extends that of Frankl and Keevash--Sudakov on the Tur\\'an density and the Tur\\'{a}n number of the $4$-uniform expanded triangle. We also show that the Tur\\'{a}n density of $C_{4k+2}^{4}$ is $1/2$ for all integers $k \\ge 2$, and establish the corresponding stability result. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22828","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22828/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}