منابع مشابه
Uniformly cross intersecting families
Let A and B denote two families of subsets of an n-element set. The pair (A,B) is said to be `-cross-intersecting iff |A∩B| = ` for all A ∈ A and B ∈ B. Denote by P`(n) the maximum value of |A||B| over all such pairs. The best known upper bound on P`(n) is Θ(2), by Frankl and Rödl. For a lower bound, Ahlswede, Cai and Zhang showed, for all n ≥ 2`, a simple construction of an `-cross-intersectin...
متن کاملOn cross-intersecting families
Frankl, P., On cross-intersecting families, Discrete Mathematics 108 (1992) 291-295. Let n 3 t z 1 be integers. Let 9, YI be families of subsets of the n-element set X. They are called cross t-intersecting if IF n GI 2 t holds for all F E 9 and G E 3. If 9 = CfI then 9 is called t-intersecting. Let m(n, t) denote the maximum possible cardinality of a r-intersecting family. Our main result says ...
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 کاملCross-Intersecting Families of Vectors
Given a sequence of positive integers p = (p1, . . . , pn), let Sp denote the family of all sequences of positive integers x = (x1, . . . , xn) such that xi ≤ pi for all i. Two families of sequences (or vectors), A,B ⊆ Sp, are said to be r-cross-intersecting if no matter how we select x ∈ A and y ∈ B, there are at least r distinct indices i such that xi = yi. We determine the maximum value of |...
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: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7162