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On the Size of the Smallest Non-Classical Blocking Set of Rédei Type in PG(2, p)

András Gács
2000 Journal of combinatorial theory. Series A  
This is equivalent to saying that besides the projective triangle, every blocking set of Rédei type in P G(2, p) has size at least 3 p−1 2 + 1 3 √ p.  ...  We prove that the number of directions determined by a set of p points in AG(2, p), p prime, can not be between p+3 2 and p−1 2 + 1 3 √ p.  ...  With the terminology of blocking sets, 2.6 can be formulated in the following way: Theorem 4.1 A blocking set of Rédei type in P G(2, p), p prime, is the projective triangle (of size p + p+3 2 ) or has  ... 
doi:10.1006/jcta.1999.2998 fatcat:n35gp326ubdhvaqbekufxsozxq

The Use of Blocking Sets in Galois Geometries and in Related Research Areas [chapter]

V. Pepe, L. Storme
2011 Springer Proceedings in Mathematics  
By showing the many applications on blocking sets, we also wish to prove that researchers who improve results on blocking sets in fact open the door to improvements on the solution of many other problems  ...  Besides their intrinsic geometrical importance, the importance of blocking sets also arises from the use of blocking sets for the solution of many other geometrical problems, and problems in related research  ...  [63] In PG(2, q 3 ), where q = p h , h ≥ 2 even, p ≥ 7, the smallest non-trivial blocking sets are: a) a Baer subplane PG(2, q 3 2 ) (hence of order q 3 + q 3 2 + 1); b) a minimal blocking set of Rédei  ... 
doi:10.1007/978-1-4614-0709-6_15 fatcat:ngfvmymvprbqfooj4do3jadnb4

Page 7953 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
of the Hermitian arcs and of the non-singular Hermitian varieties if d is even.” 2000k:51008 51E21 05B25 Gacs, Andras (H-AOS; Budapest) On the size of the smallest non-classical blocking set of Rédei  ...  The corollary says that a blocking set of Rédei type has size at least p+(p-—1)/2+./p/3 unless it is the graph of (b) together with the directions it determines. J. C.  ... 

Blocking sets of Rédei type in projective Hjelmslev planes

Ivan Landjev, Stoyan Boev
2010 Discrete Mathematics  
We construct, in Hjelmslev planes over chain rings of nilpotency index 2 that contain the residue field as a proper subring, the Baer subplanes associated with this subring as Rédei type blocking sets.  ...  In this paper, we introduce Rédei type blocking sets in projective Hjelmslev planes over finite chain rings.  ...  Acknowledgements The research of the first author was supported by the Strategic Development Fund of the New Bulgarian University under Contract 357/14.05.2009.  ... 
doi:10.1016/j.disc.2010.03.016 fatcat:eycv76ubvfedlifahuwww36pcu

On linear sets of minimum size [article]

Dibyayoti Jena, Geertrui Van de Voorde
2020 arXiv   pre-print
Our construction extends the known examples of linear sets of size q^k-1+1 in PG(1,q^h) constructed for k=h=4 [G. Bonoli and O. Polverino, 𝔽_q-Linear blocking sets in PG(2,q^4), Innov.  ...  This leads to new infinite families of small minimal blocking sets which are not of Rédei type.  ...  In particular, we thank one of the referees for pointing out the link with references [3] and [6] .  ... 
arXiv:2005.10931v2 fatcat:7nnzdwxtrnfaxl3awncvctocde

Tight sets and m-ovoids of generalised quadrangles

John Bamberg, Maska Law, Tim Penttila
2009 Combinatorica  
Blocking Sets and Semifields Guglielmo Lunardon A relationship is found between semifield spreads of P G(3, q), small Rédei minimal blocking sets of P G(2, q 2 ) disjoint from a Baer subline of the Rédei  ...  block size 2.  ... 
doi:10.1007/s00493-009-2179-x fatcat:3lv4kl6qafbfdemivsj73n6miq

The 2-Blocking Number and the Upper Chromatic Number ofPG(2,q)

Gábor Bacsó, Tamás Héger, Tamás Szőnyi
2013 Journal of combinatorial designs (Print)  
The minimum number of points in a double blocking set of Π is denoted by τ 2 (Π). Let PG(2, q) be the Desarguesian projective plane over GF(q), the finite field of q elements.  ...  A 2-fold blocking set (double blocking set) in a finite projective plane Π is a set of points, intersecting every line in at least two points.  ...  We are grateful to the anonymous referees whose suggestions highly advanced the clarity and the readability of the paper.  ... 
doi:10.1002/jcd.21347 fatcat:fkalrojogjcapn246msvlsy7vq

Integral point sets over finite fields [article]

Sascha Kurz
2008 arXiv   pre-print
We consider point sets in the affine plane F_q^2 where each Euclidean distance of two points is an element of F_q.  ...  These sets are called integral point sets and were originally defined in m-dimensional Euclidean spaces E^m. We determine their maximal cardinality I(F_q,2).  ...  Acknowledgment I am thankful to Aart Blokhuis, Stancho Diemiev, Michael Kiermaier, Harald Meyer, and Ivo Radloff whose comments were very helpful during the preparation of this article.  ... 
arXiv:0804.1289v1 fatcat:cs7irrvmxnb45enypw74fh6g44

The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems

Cornelius Greither, Radiu Kučera
2002 Annales de l'Institut Fourier  
Some identities in a group ring. Remark. -This section is technical and its details may well be skipped on the first reading.  ...  Some of the work of the first author was supported by a NSERC grant; the second author was supported by grant 201/97/0433 of the Grant Agency of the Czech Republic. 1.  ...  The classical theorem of Rédei and Reichardt determines the number of invariants divisible by 4.)  ... 
doi:10.5802/aif.1900 fatcat:wr6xmj63pbaxtevgcqcdmxocqi

On the automorphism groups of Lunardon-Polverino scattered linear sets [article]

Wei Tang, Yue Zhou, Ferdinando Zullo
2022 arXiv   pre-print
Lunardon and Polverino introduced in 2001 a new family of maximum scattered linear sets in PG(1,q^n) to construct linear minimal Rédei blocking sets.  ...  the number of inequivalent linear sets of this family.  ...  The research of Ferdinando Zullo was supported by the project "VALERE: VAnviteLli pEr la RicErca" of the University of Campania "Luigi Vanvitelli" and was partially supported by the Italian National Group  ... 
arXiv:2201.12777v1 fatcat:pg63fmiqpvfc7kadayg4qyvbi4

A SURVEY ON SEMIOVALS

Gy¨orgy Gy¨, Gy¨orgy Kiss
unpublished
. • The only semi-ovoids of PG(3, q) are the ovoids (set of q 2 + 1 points, no three of them are collinear). • In PG(n, q), n > 3, there are no semi-ovoids. 2000 Mathematics Subject Classification.  ...  Q is called semi quadratic set (SQS), if every point on a line of L belongs to P, and for all PP the union T P of all tangents to Q at P is either a hyperplane or the whole space Π.  ...  of size 3q − n − 2 in PG(2, q). (4) If q = r e , r ≥ 3, r is a prime power and e ≥ 2 then there exist blocking semiovals of size 3q − r − 2 in PG(2, q). (5) In PG(2, q), q odd, five types of blocking  ... 
fatcat:lnzk24uijnbatngpnbjqnvsuoy

Page 154 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
(English summary) 2000i:51016 — On the size of the smallest non-classical blocking set of Rédei type in PG(2, p). (English summary) 2000k:51008 Glynn, David G.  ...  (English summary) 2000c:00004 Polverino, Olga Small minimal blocking sets and complete k-arcs in PG(2, p+).  ... 

Page 1253 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
(English summary) 2000h:51014 Gacs, Andras On the size of the smallest non-classical blocking set of Rédei type in PG(2, p). (English summary) 2000k:51008 Giulietti, Massimo (with Ughi, E.)  ...  (English summary) 2000j:51007 — Small minimal blocking sets and complete k-arcs in PG(2, p*).  ... 

Blocking and double blocking sets in finite planes

Jan De Beule, Tamás Héger, Tamás Sz˝, Geertrui Van De Voorde
2016 the electronic journal of combinatorics   unpublished
bound for the size of a minimal blocking set in an affine Desarguesian plane of order q 2.  ...  As a corollary, we obtain the existence of a minimal blocking set of a non-Desarguesian affine plane of order q 2 of size at most 4q 2 /3 + 5q/3, which is considerably smaller than 2q 2 − 1, the Jamison  ...  Acknowledgment We thank Gordon Royle for his motivating question and Bence Csajbók for his help in finding the papers [7, 16] .  ... 
fatcat:kcfwruzvwrgzramrsl6e3jgjo4

Gout [chapter]

2008 Encyclopedia of Genetics, Genomics, Proteomics and Informatics  
Before a decision is made, the probabilities of a set of actions, e.g., p(1) and p(2) must be assessed, generally by a subjective manner.  ...  In Drosophila (1 X):(2 sets of auto-somes) means male, whereas (2X):(2 set of autosomes) = females (1:1).  ...  ▶phosphoinositides Grunstein-Hogness Screening: Grunstein-Hogness screening involves in situ lysis of bacterial colonies on nitrocellulose filters (or other membranes) and non-covalent attachment of the  ... 
doi:10.1007/978-1-4020-6754-9_7078 fatcat:igkfa5bydfeehhe7ekrw5dudny
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