The maximum sum and the maximum product of sizes 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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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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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...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2014
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.06.029