منابع مشابه
Enumeration of intersecting families
For a natural number m, let m =11,2, . . ., m} . An intersecting family on m is a set A of sets such that U A g m and any two members of A have non-empty intersection . We let J_ be the set of all maximal intersecting families on m . We are concerned with estimating JJ . J . In Section 2 we obtain a lower bound by elementary counting methods . In Section 3 we obtain an upper bound using a resul...
متن کاملIntersecting families of permutations
A set of permutations I ⊂ Sn is said to be k-intersecting if any two permutations in I agree on at least k points. We show that for any k ∈ N, if n is sufficiently large depending on k, then the largest kintersecting subsets of Sn are cosets of stabilizers of k points, proving a conjecture of Deza and Frankl. We also prove a similar result concerning k-cross-intersecting subsets. Our proofs are...
متن کاملIntersecting families of permutations
Let Sn be the symmetric group on the set X = {1, 2, . . . , n}. A subset S of Sn is intersecting if for any two permutations g and h in S, g(x) = h(x) for some x ∈ X (that is g and h agree on x). Deza and Frankl (J. Combin. Theory Ser. A 22 (1977) 352) proved that if S ⊆ Sn is intersecting then |S| ≤ (n − 1)!. This bound is met by taking S to be a coset of a stabiliser of a point. We show that ...
متن کاملCross-intersecting sub-families of hereditary families
Families A1,A2, . . . ,Ak of sets are said to be cross-intersecting if for any i and j in {1, 2, . . . , k} with i 6= j, any set in Ai intersects any set in Aj . For a nite set X, let 2X denote the power set of X (the family of all subsets of X). A family H is said to be hereditary if all subsets of any set in H are in H; so H is hereditary if and only if it is a union of power sets. We conject...
متن کاملChain Intersecting Families
Let F be a family of subsets of an n-element set. F is called (p,q)-chain intersecting if it does not contain chains A1 ( A2 ( · · · ( Ap and B1 ( B2 ( · · · ( Bq with Ap∩Bq = ∅. The maximum size of these families is determined in this paper. Similarly to the p = q = 1 special case (intersecting families) this depends on the notion of r-complementing-chain-pair-free families, where r = p + q − ...
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ژورنال
عنوان ژورنال: Open Mathematics
سال: 2014
ISSN: 2391-5455
DOI: 10.2478/s11533-014-0420-3