On the maximum size of Erdős-Ko-Rado sets in $$H(2d+1, q^2)$$

Ihringer, Ferdinand; Metsch, Klaus

doi:10.1007/s10623-012-9765-4

Cited by 11 publications

(12 citation statements)

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“…[3,4,11,13,14]. Given a polar space of rank d and an integer n with 1 ≤ n ≤ d, an Erdős-Ko-Rado set of subspaces of rank n of the polar space is a set of subspaces of rank n of the polar space such that any two subspaces of the set have a non-trivial intersection.…”

Section: Resultsmentioning

confidence: 99%

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An Erdős-Ko-Rado theorem for finite classical polar spaces

Metsch

2015

J Algebr Comb

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Section: Resultsmentioning

confidence: 99%

“…Presently the best known upper bound for Erdős-Ko-Rado sets of generators in these spaces was proved in [11]. Roughly speaking, the bound is one power of q larger than the size of the point-pencils.…”

Section: Results 3 ([14]mentioning

confidence: 99%

An Erdős-Ko-Rado theorem for finite classical polar spaces

Metsch

2015

J Algebr Comb

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“…In fact, in [13], the largest Erdős-Ko-Rado sets of generators were classified for all finite classical polar spaces except the Hermitian varieties H(4n + 1, q 2 ), n ≥ 2. For those, the best result was obtained in [9].…”

Section: Moreover Equality Holds If and Only Ifmentioning

confidence: 99%

The second largest Erdős–Ko–Rado sets of generators of the hyperbolic quadrics Q⁺(4n + 1, q)

Boeck

2016

Advances in Geometry

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“…Recent results on Erdős-Ko-Rado sets in projective and polar spaces can be found in e.g. [2,3,8,13,14,16,19].…”

Section: Erdős-ko-rado Theoremsmentioning

confidence: 99%

The largest Erdős–Ko–Rado sets in $$2-(v,k,1)$$ 2 - ( v , k , 1 ) designs

Boeck

2014

Des. Codes Cryptogr.

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An Erdős-Ko-Rado set in a block design is a set of pairwise intersecting blocks. In this article we study Erdős-Ko-Rado sets in 2 − (v, k, 1) designs, Steiner systems. The Steiner triple systems and other special classes are treated separately. For k ≥ 4, we prove that the largest Erdős-Ko-Rado sets cannot be larger than a point-pencil if r ≥ k 2 − 3k + 3 4 √ k + 2 and that the largest Erdős-Ko-Rado sets are point-pencils if also r = k 2 − k + 1 and (r, k) = (8, 4). For unitals we also determine an upper bound on the size of the second-largest maximal Erdős-Ko-Rado sets.

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On the maximum size of Erdős-Ko-Rado sets in $$H(2d+1, q^2)$$

Cited by 11 publications

References 5 publications

An Erdős-Ko-Rado theorem for finite classical polar spaces

An Erdős-Ko-Rado theorem for finite classical polar spaces

The second largest Erdős–Ko–Rado sets of generators of the hyperbolic quadrics Q⁺(4n + 1, q)

The largest Erdős–Ko–Rado sets in $$2-(v,k,1)$$ 2 - ( v , k , 1 ) designs

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On the maximum size of Erdős-Ko-Rado sets in $$H(2d+1, q^2)$$

Cited by 11 publications

References 5 publications

An Erdős-Ko-Rado theorem for finite classical polar spaces

An Erdős-Ko-Rado theorem for finite classical polar spaces

The second largest Erdős–Ko–Rado sets of generators of the hyperbolic quadrics Q+(4n + 1, q)

The largest Erdős–Ko–Rado sets in $$2-(v,k,1)$$ 2 - ( v , k , 1 ) designs

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The second largest Erdős–Ko–Rado sets of generators of the hyperbolic quadrics Q⁺(4n + 1, q)