Brace-Daykin type inequalities for intersecting families

Weighted Non-Trivial Multiply Intersecting Families

Let n,r and t be positive integers. A family F of subsets of [n]={1,2, . . . ,n} is called r-wise t-intersecting if |F1∩·· ·∩Fr|≥ t holds for all F1, . . . ,Fr ∈F . An r-wise 1-intersecting family is also called an r-wise intersecting family for short. An r-wise t-intersecting family F is called non-trivial if |⋂F∈F F |<t. Let us define the Brace–Daykin structure as follows. F BD = {F ⊂ [n] : |...

EKR type inequalities for 4-wise intersecting families

Let 1 ≤ t ≤ 7 be an integer and let F be a k-uniform hypergraph on n vertices. Suppose that |A∩B∩C∩D| ≥ t holds for all A,B,C,D ∈ F . Then we have |F | ≤ (n−t k−t ) if | k n − 2 |< ε holds for some ε > 0 and all n > n0(ε). We apply this result to get EKR type inequalities for “intersecting and union families” and “intersecting Sperner families.”

Some Inequalities Concerning Cross-Intersecting Families

Combinatorics, Probability and Computing / Volume 7 / Issue 03 / September 1998, pp 247 260 DOI: null, Published online: 08 September 2000 Link to this article: http://journals.cambridge.org/abstract_S0963548398003575 How to cite this article: P. FRANKL and N. TOKUSHIGE (1998). Some Inequalities Concerning Cross-Intersecting Families. Combinatorics, Probability and Computing, 7, pp 247-260 Requ...

THE EIGENVALUE METHOD FOR CROSS t-INTERSECTING FAMILIES

We show that the Erdős–Ko–Rado inequality for t-intersecting families of subsets can be easily extended to an inequality for cross t-intersecting families by using the eigenvalue method. The same applies to the case of t-intersecting families of subspaces. The eigenvalue method is one of the proof techniques to get Erdős–Ko–Rado type inequalities for t-intersecting families, for example, a proo...

Inequalities for a Pair of Maps S x S - ~ S with S a Finite Set