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An Erdős–Ko–Rado Theorem for Direct Products
Authors:P Frankl
Institution:Université Paris 6, Combinatoire, 4 place Jussieu, Paris, 75005, France
Abstract:Letni, kibe positive integers,i=1, ..., d,satisfyingni≥2ki.LetX1, ..., Xdbe pairwise disjoint sets with |Xi| =ni.LetView the MathML sourcebe the family of those (k1+···+kd)-element sets which have exactlykielements inXi, i=1,..., d.It is shown that ifView the MathML sourceView the MathML sourceis an intersecting family then |View the MathML source|/|View the MathML source|≤maxiki/ni,and this is best possible. The proof is algebraic, although in thed=2 case a combinatorial argument is presented as well.
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