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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.
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.
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
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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on the cardinalities of mshades of t(m)intersecting families of k(m)subsets of [2m], as m → ∞. A generalization to crosstintersecting families is also considered.
CROSS tINTERSECTING INTEGER SEQUENCES FROM WEIGHTED ERDŐS–KO–RADO
, 2013
"... Let m, n and t be positive integers. Consider [m] n as the set of sequences of length n on an mletter alphabet. We say that two subsets A ⊂ [m] n and B ⊂ [m] n cross tintersect if any two sequences a ∈ A and b ∈ B match in at least t positions. In this case it is shown that if m> (1 − 1 t √ 2)− ..."
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Cited by 2 (0 self)
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)−1 then AB  ≤ (m n−t) 2. We derive this result from a weighted version of the Erdős–Ko–Rado theorem concerning cross tintersecting families of subsets, and we also include the corresponding stability statement. One of our main tools is the eigenvalue method for intersection matrices due to Friedgut [10].
Rho GTPases and the actin cytoskeleton
 Science
, 1998
"... The actin cytoskeleton mediates a variety of essential biological functions in all eukaryotic cells. In addition to providing a structural framework around which cell shape and polarity are defined, its dynamic properties provide the driving force for cells to move and to divide. Understanding the b ..."
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Cited by 615 (4 self)
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the biochemical mechanisms that control the organization of actin is thus a major goal of contemporary cell biology, with implications for health and disease. Members of the Rho family of small guanosine triphosphatases have emerged as key regulators of the actin cytoskeleton, and furthermore, through
On crossintersecting families of sets
 Graphs Combin
"... Abstract. A family A of ‘element subsets and a family B of kelement subsets of an nelement set are crossintersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product jAjjBj, a ..."
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Cited by 9 (0 self)
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Abstract. A family A of ‘element subsets and a family B of kelement subsets of an nelement set are crossintersecting if every set from A has a nonempty intersection with every set from B. We compare two previously established inequalities each related to the maximization of the product j
Crossintersecting families of permutations
 J. Combin. Theory Ser. A
, 2010
"... Abstract For positive integers r and n with r ≤ n, let P r,n be the family of all sets ..."
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Cited by 9 (4 self)
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Abstract For positive integers r and n with r ≤ n, let P r,n be the family of all sets
Uniformly cross intersecting families
, 2006
"... Let A and B denote two families of subsets of an nelement set. The pair (A, B) is said to be ℓcrossintersecting iff A∩B  = ℓ for all A ∈ A and B ∈ B. Denote by Pℓ(n) the maximum value of AB  over all such pairs. The best known upper bound on Pℓ(n) is Θ(2n), by Frankl and Rödl. For a lower ..."
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Cited by 1 (0 self)
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Let A and B denote two families of subsets of an nelement set. The pair (A, B) is said to be ℓcrossintersecting iff A∩B  = ℓ for all A ∈ A and B ∈ B. Denote by Pℓ(n) the maximum value of AB  over all such pairs. The best known upper bound on Pℓ(n) is Θ(2n), by Frankl and Rödl. For a lower
Results 1  10
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