The maximum product of weights of cross-intersecting families
نویسندگان
چکیده
منابع مشابه
The maximum sum and the maximum product of sizes of cross-intersecting families
We say that a set A t-intersects a set B if A and B have at least t common elements. A family A of sets is said to be t-intersecting if each set in A t-intersects any other set in A. Families A1,A2, ...,Ak are said to be cross-t-intersecting if for any i and j in {1, 2, ..., k} with i 6= j, any set in Ai t-intersects any set in Aj . We prove that for any finite family F that has at least one se...
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Two families A and B of sets are said to be cross-intersecting if each set in A intersects each set in B. For any two integers n and k with 1 6 k 6 n, let ([n] 6k ) denote the family of subsets of {1, . . . , n} of size at most k, and let Sn,k denote the family of sets in ([n] 6k ) that contain 1. The author recently showed that if A ⊆ ( [m] 6r ) , B ⊆ ( [n] 6s ) , and A and B are cross-interse...
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We verify a conjecture of Hirschorn concerning the maximum product of sizes of cross-t-intersecting uniform families. We say that a set A t-intersects a set B if A and B have at least t common elements. Two families A and B of sets are said to be cross-t-intersecting if each set in A t-intersects each set in B. For any positive integers n and r, let ([n] r ) denote the family of all r-element s...
متن کاملThe maximum sum and product of sizes of cross-intersecting families
A family A of sets is said to be t-intersecting if any two distinct sets in A have at least t common elements. Families A1,A2, ...,Ak are said to be cross-t-intersecting if for any i and j in {1, 2, ..., k} with i 6= j, any set in Ai intersects any set in Aj on at least t elements. We prove that for any finite family F that has at least one set of size at least t, there exists an integer k0 ≤ |...
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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...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2016
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms/jdw067