{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FJ7PZV5UAVYLJDVFXSFY5RNYOR","short_pith_number":"pith:FJ7PZV5U","schema_version":"1.0","canonical_sha256":"2a7efcd7b40570b48ea5bc8b8ec5b874659ae6d456c808be90b4e8a618c42303","source":{"kind":"arxiv","id":"2608.04615","version":1},"attestation_state":"computed","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 $0t\\ge1$ 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