{"paper":{"title":"The $(t,p)$-Norm in Classical Extremal Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiamiao Zhao, Yuanpei Wang","submitted_at":"2026-08-05T09:20:20Z","abstract_excerpt":"Given integers $r>t\\ge1$ and a real number $p>0$, the $(t,p)$-norm $||\\mathcal{H}||_{t,p}$ of an $r$-graph $\\mathcal{H}$ is the sum of the $p$-th powers of the degrees $d_{\\mathcal{H}}(T)$ over all $t$-subsets $T\\subseteq V(\\mathcal{H})$. When $t=r-1$, this is the codegree $p$-norm. For all sufficiently large $n$, we obtain the following results. The first two apply in both the convex range $p>1$ and the concave range $0<p<1$. First, for $r$-graphs with matching number at most $s$, we determine the maximum $(t,p)$-norm. Second, for $k$-intersecting families, we establish an Erd\\H{o}s--Ko--Rado"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04615","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/2608.04615/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"}