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...
متن کاملThe maximum product of sizes of cross-t-intersecting uniform families
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 ≤ |...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2017
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.04.019