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

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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