Forbidding just one intersection, for permutations
نویسندگان
چکیده
منابع مشابه
Forbidding Just One Intersection
Following a conjecture of P. Erdos, we show that if 9 is a family of k-subsets of an n-set no two of which intersect in exactly I elements then for k 2 21+ 2 and n sufficiently large IF:/ < (;:‘,I:) with equality holding if and only if 9 consists of all the k-sets containing a fixed (I+ I)-set. In general we show 19) <dknmax(‘.k-‘-l), where dk is a constant depending only on k. These results ar...
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A family A ⊂ P[n] is said to be an antichain if A 6⊂ B for all distinct A,B ∈ A. A classic result of Sperner shows that such families satisfy |A| ≤ ( n bn/2c ) , which is easily seen to be best possible. One can view the antichain condition as a restriction on the intersection sizes between sets in different layers of P[n]. More generally one can ask, given a collection of intersection restrict...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2014
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2014.04.011