Intersecting families of permutations
نویسندگان
چکیده
منابع مشابه
Intersecting 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 کاملIntersecting families of permutations and partial permutations
The above result motivated the study of intersecting families of permutations which was initiated by Deza and Frankl, see [2]. Let Sn be the symmetric group on [n], that is the group of all permutations of [n]. For a positive integer t, a subset A of Sn is said to be t-intersecting if, for any g, h ∈ A with g 6= h, we have |{x : g(x) = h(x)}| ≥ t. By an intersecting family, we mean an 1-interse...
متن کاملSetwise intersecting families of permutations
A family of permutations A ⊂ Sn is said to be t-set-intersecting if for any two permutations σ, π ∈ A, there exists a t-set x whose image is the same under both permutations, i.e. σ(x) = π(x). We prove that if n is sufficiently large depending on t, the largest t-set-intersecting families of permutations in Sn are cosets of stabilizers of t-sets. The t = 2 case of this was conjectured by János ...
متن کاملCross-intersecting families of permutations
For positive integers r and n with r ≤ n, let Pr,n be the family of all sets {(1, y1), (2, y2), ..., (r, yr)} such that y1, y2, ..., yr are distinct elements of [n] = {1, 2, ..., n}. Pn,n describes permutations of [n]. For r < n, Pr,n describes permutations of relement subsets of [n]. Families A1,A2, ...,Ak of sets are said to be cross-intersecting if, for any distinct i and j in [k], any set i...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2003
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(03)00078-7