{"paper":{"title":"Nondegenerate Tur\\'{a}n problems under $(t,p)$-norms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel I\\v{l}kovi\\v{c}, Jared Le\\'on, Oleg Pikhurko, Wanfang Chen, Xizhi Liu","submitted_at":"2024-06-22T20:35:41Z","abstract_excerpt":"Given integers $r > t \\ge 1$ and a real number $p > 0$, the $(t,p)$-norm $\\left\\lVert \\mathcal{H} \\right\\rVert_{t,p}$ of an $r$-graph $\\mathcal{H}$ is the sum of the $p$-th power of the degrees $d_{\\mathcal{H}}(T)$ over all $t$-subsets $T \\subset V(\\mathcal{H})$. We conduct a systematic study of the Tur\\'{a}n-type problem of determining $\\mathrm{ex}_{t,p}(n,\\mathcal{F})$, which is the maximum of $\\left\\lVert \\mathcal{H} \\right\\rVert_{t,p}$ over all $n$-vertex $\\mathcal{F}$-free $r$-graphs $\\mathcal{H}$.\n  We establish several basic properties for the $(t,p)$-norm of $r$-graphs, enabling us to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.15934","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/2406.15934/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"}