For large n, every extremal family with no s+1 pairwise <t-intersecting k-sets is a union of s t-intersecting cliques, as predicted by the Ahlswede-Khachatrian analogy.
Frankl, The Erd˝ os-Ko-Rado theorem is true for n=ckt, Combinatorics (Proc
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The Hajnal--Rothschild problem
For large n, every extremal family with no s+1 pairwise <t-intersecting k-sets is a union of s t-intersecting cliques, as predicted by the Ahlswede-Khachatrian analogy.