An Erdős–Ko–Rado theorem for partial permutations

Ku, Cheng Yeaw; Leader, Imre

doi:10.1016/j.disc.2005.11.007

Cited by 38 publications

(34 citation statements)

References 6 publications

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“…Ku and Leader [27] proved that S * is also strictly EKR for the few remaining values of r. This was settled by Li and Wang [29] using tools forged by Ku and Leader.…”

Section: Intersecting Families Of Permutations and Partial Permutationsmentioning

confidence: 91%

On t-intersecting families of signed sets and permutations

Borg

2009

Discrete Mathematics

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“…Ku and Leader [27] proved that S * is also strictly EKR for the few remaining values of r. This was settled by Li and Wang [29] using tools forged by Ku and Leader.…”

Section: Intersecting Families Of Permutations and Partial Permutationsmentioning

confidence: 91%

On t-intersecting families of signed sets and permutations

Borg

2009

Discrete Mathematics

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“…For example, intersecting families of permutations were initiated by Deza and Frankl in [6]. Some recent work done on this problem and its variants can be found in [3,5,7,11,12,14,16,[21][22][23]27]. The Erdős-Ko-Rado type results also appear for set partitions [15,18,17] and for weak compositions [19].…”

Section: Then Equality Holds If and Only Ifmentioning

confidence: 96%

Onr-crosst-intersecting families for weak compositions

Wong

2015

Discrete Mathematics

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a b s t r a c tLet N 0 be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., P (n, l) Suppose that l ≥ t + 2. We prove that there exists a constant n 0 = n 0 (l 1 , l 2 , . . . , l r , t) depending only on l j 's and t, such that for all n j ≥ n 0 , if the families A j ⊆ P(n j , l j ) (j = 1, 2, . . . , r) are r-cross t-intersecting, thenMoreover, equality holds if and only if there is a t-set T of {1, 2, . . . , l} such that A j = {u ∈ P(n j , l j ) : u(i) = 0 for all i ∈ T } for j = 1, 2, . . . , r.

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“…Recently, Ku and Leader [11] established an EKR theorem for partial permutations. An r-partial permutation of [n] is a pair (A, f ) where A ⊂ [n] is an r-set and f : A → [n] is an injective map.…”

Section: Ys LImentioning

confidence: 99%

An Erdös-Ko-Rado theorem for restricted signed sets

2009

Acta Math. Appl. Sin. Engl. Ser.

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A restricted signed r-set is a pair (A, f ), where A ⊆ [n] = {1, 2, · · · , n} is an r-set and f is a map from A to [n] with f (i) = i for all i ∈ A. For two restricted signed sets (A, f ) and (B, g), we define an order as (A, f ) ≤ (B, g) if A ⊆ B and g| A = f . A family A of restricted signed sets on [n] is an intersecting antichain if for any (A, f ), (B, g) ∈ A, they are incomparable and there exists x ∈ A ∩ B such that f (x) = g(x). In this paper, we first give a LYM-type inequality for any intersecting antichain A of restricted signed sets, from which we then obtain |A| ≤ n−1 r−1 (n − 1) r−1 if A consists of restricted signed r-sets on [n]. Unless r = n = 3, equality holds if and only if A consists of all restricted signed r-sets (A, f ) such that x 0 ∈ A and f (x 0 ) = ε 0 for some fixed x 0 ∈ [n], ε 0 ∈ [n] \ {x 0 }.

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An Erdős–Ko–Rado theorem for partial permutations

Cited by 38 publications

References 6 publications

On t-intersecting families of signed sets and permutations

On t-intersecting families of signed sets and permutations

Onr-crosst-intersecting families for weak compositions

An Erdös-Ko-Rado theorem for restricted signed sets

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