3-setwise intersecting families of the symmetric group
نویسندگان
چکیده
Given two positive integers n?3 and t?n, the permutations ?,??Sym(n) are t-setwise intersecting if they agree (setwise) on a t-subset of {1,2,…,n}. A family F?Sym(n) is any F intersecting. Ellis (2012) [6] conjectured that t?n family, then |F|?t!(n?t)! equality holds only coset setwise stabilizer In this paper, we prove n?11 3-setwise intersecting, |F|?6(n?3)!. Moreover, characteristic vector maximum size lies in sum eigenspaces induced by permutation module Sym(n) acting 3-subsets
منابع مشابه
Setwise 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 ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2021
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2021.112467