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

2000
*
Journal of combinatorial theory. Series A
*

This is equivalent to saying that besides

doi:10.1006/jcta.1999.2998
fatcat:n35gp326ubdhvaqbekufxsozxq
*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 ...##
###
The Use of Blocking Sets in Galois Geometries and in Related Research Areas
[chapter]

2011
*
Springer Proceedings in Mathematics
*

By showing

doi:10.1007/978-1-4614-0709-6_15
fatcat:ngfvmymvprbqfooj4do3jadnb4
*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*...##
###
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

2010
*
Discrete Mathematics
*

We construct,

doi:10.1016/j.disc.2010.03.016
fatcat:eycv76ubvfedlifahuwww36pcu
*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. ...##
###
On linear sets of minimum size
[article]

2020
*
arXiv
*
pre-print

Our construction extends

arXiv:2005.10931v2
fatcat:7nnzdwxtrnfaxl3awncvctocde
*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] . ...##
###
Tight sets and m-ovoids of generalised quadrangles

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*. ...

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

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. ...

##
###
Integral point sets over finite fields
[article]

2008
*
arXiv
*
pre-print

We consider point

arXiv:0804.1289v1
fatcat:cs7irrvmxnb45enypw74fh6g44
*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. ...##
###
The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems

2002
*
Annales de l'Institut Fourier
*

Some identities

doi:10.5802/aif.1900
fatcat:wr6xmj63pbaxtevgcqcdmxocqi
*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.) ...##
###
On the automorphism groups of Lunardon-Polverino scattered linear sets
[article]

2022
*
arXiv
*
pre-print

Lunardon and Polverino introduced

arXiv:2201.12777v1
fatcat:pg63fmiqpvfc7kadayg4qyvbi4
*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 ...##
###
A SURVEY ON SEMIOVALS

unpublished

. •

fatcat:lnzk24uijnbatngpnbjqnvsuoy
*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*P*∈*P**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*...##
###
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

2016
*
the electronic journal of combinatorics
*
unpublished

bound for

fatcat:kcfwruzvwrgzramrsl6e3jgjo4
*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] . ...##
###
Gout
[chapter]

2008
*
Encyclopedia of Genetics, Genomics, Proteomics and Informatics
*

Before a decision is made,

doi:10.1007/978-1-4020-6754-9_7078
fatcat:igkfa5bydfeehhe7ekrw5dudny
*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*...
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