Almost-Baer subplanes of free projective planes

1978 ◽  
Vol 7 (4) ◽  
Author(s):  
Don Row
Keyword(s):  
Projective Planes ◽  
Baer Subplanes

scholarly journals Baer subplanes of projective planes.

1975 ◽  
Author(s):  
Rilla Nichols
Keyword(s):  
Projective Planes ◽  
Baer Subplanes

scholarly journals Blocking and Double Blocking Sets in Finite Planes

10.37236/5717 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Jan De Beule ◽  
Tamás Héger ◽  
Tamás Szőnyi ◽  
Geertrui Van de Voorde
Keyword(s):  
Projective Planes ◽  
Blocking Set ◽  
Blocking Sets ◽  
Desarguesian Plane ◽  
Baer Subplanes ◽  
Desarguesian Projective Planes ◽  
Finite Planes ◽  
Value Sets ◽  
Minimal Blocking ◽  
Desarguesian Affine Plane

In this paper, by using properties of Baer subplanes, we describe the construction of a minimal blocking set in the Hall plane of order $q^2$ of size $q^2+2q+2$ admitting $1-$, $2-$, $3-$, $4-$, $(q+1)-$ and $(q+2)-$secants. 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 bound for the size of a minimal blocking set in an affine Desarguesian plane of order $q^2$.We also consider particular André planes of order $q$, where $q$ is a power of the prime $p$, and give a construction of a small minimal blocking set which admits a secant line not meeting the blocking set in $1$ mod $p$ points. Furthermore, we elaborate on the connection of this problem with the study of value sets of certain polynomials and with the construction of small double blocking sets in Desarguesian projective planes; in both topics we provide some new results.

Baer subplanes of affine and projective planes

1972 ◽  
Vol 126 (4) ◽  
pp. 339-344 ◽  
Author(s):  
Judita Cofman
Keyword(s):  
Projective Planes ◽  
Baer Subplanes

Baer subplanes and Baer collineations of derivable projective planes

1975 ◽  
Vol 44 (1) ◽  
pp. 187-192 ◽  
Author(s):  
Judita Cofman
Keyword(s):  
Projective Planes ◽  
Baer Subplanes

Spiky projective planes

1991 ◽  
Vol 257 (1-2) ◽  
pp. 51-55
Author(s):  
D. Johnston
Keyword(s):  
Projective Planes

scholarly journals On the Construction of Finite Projective Planes from Homology Semibiplanes

1990 ◽  
Vol 11 (6) ◽  
pp. 589-600
Author(s):  
G. Eric Moorhouse
Keyword(s):  
Projective Planes ◽  
Finite Projective Planes

scholarly journals On submaximal curves in fake projective planes

2021 ◽  
Vol 225 (10) ◽  
pp. 106709
Author(s):  
Piotr Pokora ◽  
Halszka Tutaj-Gasińska
Keyword(s):  
Projective Planes

4-Dimensional projective planes of Lenz type III

1972 ◽  
Vol 1 (1) ◽  
Author(s):  
Helmut Salzmann
Keyword(s):  
Projective Planes ◽  
Type Iii

scholarly journals Maximal arcs in projective planes of order 16 and related designs

2019 ◽  
Vol 19 (3) ◽  
pp. 345-351 ◽  
Author(s):  
Mustafa Gezek ◽  
Vladimir D. Tonchev ◽  
Tim Wagner
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Maximal Arcs ◽  
Even Order

Abstract The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising from maximal (120,8)-arcs, and the 2-(52,4,1) designs arising from previously known maximal (52,4)-arcs, as well as some newly discovered maximal (52,4)-arcs in the known projective planes of order 16, are computed. It is shown that each 2-(120,8,1) design associated with a maximal (120,8)-arc is embeddable in a unique way in a projective plane of order 16. This result suggests a possible strengthening of the Bose–Shrikhande theorem about the embeddability of the complement of a hyperoval in a projective plane of even order. The computations of the maximal sets of compatible resolutions of the 2-(52,4,1) designs associated with maximal (52,4)-arcs show that five of the known projective planes of order 16 contain maximal arcs whose associated designs are embeddable in two nonisomorphic planes of order 16.

scholarly journals Configurations in projective planes and quadrilateral-star Ramsey numbers

2008 ◽  
Vol 308 (17) ◽  
pp. 3986-3991 ◽  
Author(s):  
E.L. Monte Carmelo
Keyword(s):  
Projective Planes ◽  
Ramsey Numbers
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