{"paper":{"title":"Generalized Tur\\'an problem for directed cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Grzesik, Bart{\\l}omiej Kielak, Justyna Jaworska, Piotr Kuc, Tomasz \\'Slusarczyk","submitted_at":"2025-05-28T10:02:29Z","abstract_excerpt":"For integers $k, \\ell \\geq 3$, let $\\mathrm{ex}(n, \\overrightarrow{C_k}, \\overrightarrow{C_\\ell})$ denote the maximum number of directed cycles of length $k$ in any oriented graph on $n$ vertices which does not contain a directed cycle of length $\\ell$. We establish the order of magnitude of $\\mathrm{ex}(n, \\overrightarrow{C_k}, \\overrightarrow{C_\\ell})$ for every $k$ and $\\ell$ and determine its value up to a lower error term when $k \\nmid \\ell$ and $\\ell$ is large enough. Additionally, we calculate the value of $\\mathrm{ex}(n, \\overrightarrow{C_k}, \\overrightarrow{C_\\ell})$ for some other sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22189","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/2505.22189/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"}