3-setwise intersecting families of the symmetric group

Behajaina, Angelot; Roghayeh, Maleki,; Rasoamanana, Aina Toky; Sarobidy, Razafimahatratra, Andriaherimanana

doi:10.1016/j.disc.2021.112467

Cited by 7 publications

(3 citation statements)

References 18 publications

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“…This approach has been used for other simply transitive groups, such as the transitive action of Sym(n) on both ordered and unordered tuples in [12,13], for n sufficiently large. This approach is also effectively used for the action of Sym(n) on pairs [24] and 3-sets [9] of [n] for all n ≥ 5.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Some Erdös-Ko-Rado results for linear and affine groups of degree two

Meagher

Sarobidy

2022

Art Discrete Appl. Math.

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In this paper, we show that both the general linear group GL(2, q) and the special linear group SL(2, q) have both the EKR property and the EKR-module property. This is done using an algebraic method; a weighted adjacency matrix for the derangement graph for the group is found and Hoffman's ratio bound is applied to this matrix. We also consider the group AGL(2, q) and the 2-intersecting sets in PGL(2, q)

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Section: Accepted Manuscriptmentioning

confidence: 99%

Some Erdös-Ko-Rado results for linear and affine groups of degree two

Meagher

Sarobidy

2022

Art Discrete Appl. Math.

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“…We are now going to see that this property of C implies that Γ G(C) is a complete multipartite graph. To prove this, it is enough to show that F(G(C)) = H (see (1)) and that H is derangement-free. Let g ∈ G(C) be a permutation fixing (0, 0) ∈ Ω p,q .…”

Section: Cyclic Codes and Complete Multipartite Derangement Graphsmentioning

confidence: 99%

“…In [17], a measure for intersecting sets in transitive groups was introduced. Formally, the intersection density of a transitive group G ≤ Sym(Ω) is the rational number ρ(G) := max {ρ(F ) | F ⊂ G is intersecting} , where ρ(F ) := |F | |Gω| for any intersecting set F and G ω is the point stabilizer of ω ∈ Ω in G. The study of intersection density in transitive groups has recently drawn the attention of many researchers [1,11,12,13,18,19,21,22,20,24,26].…”

Section: Introductionmentioning

confidence: 99%

Intersection density of imprimitive groups of degree $pq$

Behajaina¹,

Roghayeh²,

Sarobidy³

2022

Preprint

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A subset F of a finite transitive group G ≤ Sym(Ω) is intersecting if any two elements of F agree on an element of Ω. The intersection density of G is the number ρ(G) = max |F | |G|/|Ω| | F ⊂ G is intersecting . Recently, Hujdurović et al. [11] disproved a conjecture of Meagher et al. [21, Conjecture 6.6 (3)]by constructing equidistant cyclic codes which yield transitive groups of degree pq, where p = q k −1 q−1 and q are odd primes, and whose intersection density equal to q.In this paper, we use the cyclic codes given by Hujdurović et al. and their permutation automorphisms to construct a family of transitive groups G of degree pq with ρ(G) = q k , whenever k < q < p = q k −1 q−1 are odd primes. Moreover, we extend their construction using cyclic codes of higher dimension to obtain a new family of transitive groups of degree a product of two odd primes q < p = q k −1 q−1 , and whose intersection density are equal to q. Finally, we prove that if G ≤ Sym(Ω) of degree a product of two arbitrary odd primes p > q and ω∈Ω Gω is a proper subgroup, then ρ(G) ∈ {1, q}.

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On the Second Eigenvalue of Certain Cayley Graphs on the Symmetric Group

Roghayeh

Sarobidy

2023

Bull. Malays. Math. Sci. Soc.

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3-setwise intersecting families of the symmetric group

Cited by 7 publications

References 18 publications

Some Erdös-Ko-Rado results for linear and affine groups of degree two

Some Erdös-Ko-Rado results for linear and affine groups of degree two

Intersection density of imprimitive groups of degree $pq$

On the Second Eigenvalue of Certain Cayley Graphs on the Symmetric Group

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