Non-trivial d-wise intersecting families
نویسندگان
چکیده
For an integer d?2, a family F of sets is d-wise intersecting if for any distinct A1,A2,…,Ad?F, A1?A2?…?Ad??, and non-trivial ?A?FA=?. Hilton Milner conjectured that k?d?2 large enough n, the extremal (i.e. largest) k-element subsets [n] is, up to isomorphism, one following two families:A(k,d)={A?([n]k):|A?[d+1]|?d}H(k,d)={A?([n]k):[d?1]?A,A?[d,k+1]??}?{[k+1]?{i}:i?[d?1]}. The celebrated Hilton-Milner Theorem states H(k,2) unique, k>3. We prove conjecture stability theorem, stating subfamily A(k,d) or H(k,d).
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2021
ISSN: ['0097-3165', '1096-0899']
DOI: https://doi.org/10.1016/j.jcta.2020.105369