The spectrum of minimal blocking sets

Innamorati, Stefano; Maturo, Antonio

doi:10.1016/s0012-365x(99)00082-5

Cited by 6 publications

(8 citation statements)

References 12 publications

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“…Many authors have dealt with the search of blocking sets, especially in projective planes, (see, e.g., [2], [3], [4], [5], [6], [8], [9], [10], [11], [12], [22], [23], [24], [35], [37]). Definition 4.4.…”

Section: If the Intersection Property Holds Then There Are Not Blockimentioning

confidence: 99%

“…• the blocking sets on π 7 are classified in papers of Innamorati and Maturo (see [22], [23], [24]). If k is the cardinality of a minimal blocking set on π 7 we have 12 ≤ k ≤ 19.…”

Section: If the Intersection Property Holds Then There Are Not Blockimentioning

confidence: 99%

“…In the general case there are the following results ( [22], [23], [24]), [29]): Theorem 6.3. A sufficient condition for the existence of a minimal blocking set with 3q − 4 points on a non-Desarguesian plane π q is that π q contains a proper subplane of order two.…”

Section: If the Intersection Property Holds Then There Are Not Blockimentioning

confidence: 99%

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Finite Geometric Spaces, Steiner Systems and Cooperative Games

Maturo

2014

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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Section: If the Intersection Property Holds Then There Are Not Blockimentioning

confidence: 99%

“…• the blocking sets on π 7 are classified in papers of Innamorati and Maturo (see [22], [23], [24]). If k is the cardinality of a minimal blocking set on π 7 we have 12 ≤ k ≤ 19.…”

Section: If the Intersection Property Holds Then There Are Not Blockimentioning

confidence: 99%

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Finite Geometric Spaces, Steiner Systems and Cooperative Games

Maturo

2014

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…This blocking set has a very nice structure: it consists of three disjoint Baer subplanes and two extra points. More results on the spectrum of minimal blocking sets in planes of small order can be found in Innamorati [14] and Innamorati and Maturo [15].…”

Section: Introductionmentioning

confidence: 96%

On large minimal blocking sets in PG(2,q)

Szőnyi¹,

Cossidente²,

Gács³

et al. 2004

J of Combinatorial Designs

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The size of large minimal blocking sets is bounded by the Bruen-Thas upper bound. The bound is sharp when q is a square. Here the bound is improved if q is a non-square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non-prime order. The construction can be regarded as a generalization of Buekenhout's construction of unitals. For example, if q is a cube, then our construction gives minimal blocking sets of size q 4=3 þ 1 or q 4=3 þ 2. Density results for the spectrum of minimal blocking sets in Galois planes of non-prime order is also presented. The most attractive case is when q is a square, where we show that there is a minimal blocking set for any size from the interval ½4q log q; q ffiffi ffi q p À q þ 2 ffiffi ffi q p . #

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“…The first such result is due to Bruen and Thas [4]. More results on the spectrum of minimal blocking sets in planes of small order can be found in Cossidente, Gács et alt [5] Innamorati [8],Inamorati and Maturo [9].…”

Section: Introductionmentioning

confidence: 97%

Blocking sets in the complement of hyperplane arrangements in projective space

Settepanella¹

2009

Journal of Discrete Mathematical Sciences and Cryptography

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It is well know that the theory of minimal blocking sets is studied by several author. Another theory which is also studied by a large number of researchers is the theory of hyperplane arrangements. We can remark that the affine space AG(n, q) is the complement of the line at infinity in P G(n, q). Then AG(n, q) can be regarded as the complement of an hyperplane arrangement in P G(n, q)! Therefore the study of blocking sets in the affine space AG(n, q) is simply the study of blocking sets in the complement of a finite arrangement in P G(n, q). In this paper the author generalizes this remark starting to study the problem of existence of blocking sets in the complement of a given hyperplane arrangement in P G(n, q). As an example she solves the problem for the case of braid arrangement. Moreover she poses significant questions on this new and interesting problem.

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The spectrum of minimal blocking sets

Cited by 6 publications

References 12 publications

Finite Geometric Spaces, Steiner Systems and Cooperative Games

Finite Geometric Spaces, Steiner Systems and Cooperative Games

On large minimal blocking sets in PG(2,q)

Blocking sets in the complement of hyperplane arrangements in projective space

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