Many Cliques in Bounded-Degree Hypergraphs

Recently Chase determined the maximum possible number of cliques size in a graph on vertices with given degree. Soon afterward, Chakraborti and Chen answered version this question which we ask that have edges fixed degree (without imposing any constraint vertices). In paper address these problems hypergraphs. For -graphs issues arise do not appear case. instance, for general can assign degrees to -subset vertex set . We establish bounds -cliques an -graph -degree bounded by three contexts: has vertices; (hyper)edges; (generalizing previous case) some When is special form characterize extremal prove are tight. These examples shadows either Steiner systems or partial systems. On way proving our uniqueness results, extend results Füredi Griggs Kruskal–Katona from shadow case clique