The term $k_t^{(r)}$ represents a hypergraph parameter that signifies the minimum number of edges in a $r$-uniform hypergraph that guarantees the presence of a complete sub-hypergraph with $t$ vertices. This concept is fundamental in extremal combinatorics as it helps in understanding how large a hypergraph must be to ensure certain structures exist within it. This term is closely related to Turán's theorem, which addresses the conditions under which specific configurations emerge in graphs and hypergraphs.
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