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The eigenvalue method for cross tintersecting families
, 2012
"... We show that the Erdős–Ko–Rado inequality for tintersecting families of subsets can be easily extended to an inequality for cross tintersecting families by using the eigenvalue method. The same applies to the case of tintersecting families of subspaces. ..."
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Cited by 9 (3 self)
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We show that the Erdős–Ko–Rado inequality for tintersecting families of subsets can be easily extended to an inequality for cross tintersecting families by using the eigenvalue method. The same applies to the case of tintersecting families of subspaces.
Stability for tintersecting families of permutations
, 2009
"... A family of permutations A ⊂ Sn is said to be tintersecting if any two permutations in A agree on at least t points, i.e. for any σ, π ∈ A, {i ∈ [n] : σ(i) = π(i)}  ≥ t. It was proved by Friedgut, Pilpel and the author in [6] that for n sufficiently large depending on t, a tintersecting family ..."
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Cited by 16 (6 self)
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A family of permutations A ⊂ Sn is said to be tintersecting if any two permutations in A agree on at least t points, i.e. for any σ, π ∈ A, {i ∈ [n] : σ(i) = π(i)}  ≥ t. It was proved by Friedgut, Pilpel and the author in [6] that for n sufficiently large depending on t, a tintersecting
ASYMPTOTIC UPPER BOUNDS ON THE SHADES OF tINTERSECTING FAMILIES
, 2008
"... We examine the mshades of tintersecting families of ksubsets of [n], and conjecture on the optimal upper bound on their cardinalities. This conjecture extends Frankl’s General Conjecture that was proven true by Ahlswede–Khachatrian. From this we deduce the precise asymptotic upper bounds on the ..."
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Cited by 2 (1 self)
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We examine the mshades of tintersecting families of ksubsets of [n], and conjecture on the optimal upper bound on their cardinalities. This conjecture extends Frankl’s General Conjecture that was proven true by Ahlswede–Khachatrian. From this we deduce the precise asymptotic upper bounds
ON CROSS tINTERSECTING FAMILIES OF SETS
, 2010
"... For all p,t with 0 < p < 0.11 and 1 ≤ t ≤ 1/(2p), there exists n0 such that for all n,k with n> n0 and k/n = p the following holds: if A and B are kuniform families on n vertices, and A ∩ B  ≥ t holds for all A ∈ A and B ∈ B, then A B  ≤ ( n−t) 2. k−t 1. ..."
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Cited by 7 (3 self)
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For all p,t with 0 < p < 0.11 and 1 ≤ t ≤ 1/(2p), there exists n0 such that for all n,k with n> n0 and k/n = p the following holds: if A and B are kuniform families on n vertices, and A ∩ B  ≥ t holds for all A ∈ A and B ∈ B, then A B  ≤ ( n−t) 2. k−t 1.
The maximum size of 3wise tintersecting families
 European J. Combin
"... Dedicated to Professor Hikoe Enomoto on the occasion of his sixtieth birthday ABSTRACT. Let t ≥ 26 and let F be a kuniform hypergraph on n vertices. Suppose that F1 ∩ F2 ∩ F3  ≥ t holds for all F1,F2,F3 ∈ F. We prove that the size of F is at most �n−t � k k−t if p = n satisfies 2 p ≤ √ ..."
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Cited by 7 (7 self)
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Dedicated to Professor Hikoe Enomoto on the occasion of his sixtieth birthday ABSTRACT. Let t ≥ 26 and let F be a kuniform hypergraph on n vertices. Suppose that F1 ∩ F2 ∩ F3  ≥ t holds for all F1,F2,F3 ∈ F. We prove that the size of F is at most �n−t � k k−t if p = n satisfies 2 p ≤ √
An ErdősKoRado theorem for cross tintersecting families
, 2013
"... Two families A and B, of ksubsets of an nset, are cross tintersecting if for every choice of subsets A ∈ A and B ∈ B we have A∩B  ≥ t. We address the following conjectured cross tintersecting version of the Erdős– Ko–Rado Theorem: For all n ≥ (t + 1)(k − t + 1) the maximum value of AB for ..."
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Cited by 1 (1 self)
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Two families A and B, of ksubsets of an nset, are cross tintersecting if for every choice of subsets A ∈ A and B ∈ B we have A∩B  ≥ t. We address the following conjectured cross tintersecting version of the Erdős– Ko–Rado Theorem: For all n ≥ (t + 1)(k − t + 1) the maximum value of A
NOTES FOR tINTERSECTING FAMILY This is a summary for paper [1].
"... Theorem 1 (EKR,Frankl,Wilson). Given 1 t k, and suppose n (k t+ 1)(t+ 1), then the maximal size of a tintersecting family is nt kt, uniquely (up to isomorphism) achieved by the [t]star. Clearly when 2k n + t, then the family ([n]k) is itself tintersecting. The present paper studies all other ..."
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Theorem 1 (EKR,Frankl,Wilson). Given 1 t k, and suppose n (k t+ 1)(t+ 1), then the maximal size of a tintersecting family is nt kt, uniquely (up to isomorphism) achieved by the [t]star. Clearly when 2k n + t, then the family ([n]k) is itself tintersecting. The present paper studies all
Intersecting families — uniform versus weighted
 Ryukyu Math. J
"... ABSTRACT. What is the maximal size of kuniform rwise tintersecting families? We show that this problem is essentially equivalent to determine the maximal weight of nonuniform rwise tintersecting families. Some EKR type examples and their applications are included. 1. ..."
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Cited by 9 (8 self)
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ABSTRACT. What is the maximal size of kuniform rwise tintersecting families? We show that this problem is essentially equivalent to determine the maximal weight of nonuniform rwise tintersecting families. Some EKR type examples and their applications are included. 1.
Results 1  10
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