Geodesic
A combinatorial approach to the known projective planes of order nine
Mathematica Bohemica, Tome 120 (1995) no. 4, pp. 347-366

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
A combinatorial characterization of finite projective planes using strongly canonical forms of incidence matrices is presented. The corresponding constructions are applied to known projective planes of order 9. As a result a new description of the Hughes plane of order nine is obtained.
A combinatorial characterization of finite projective planes using strongly canonical forms of incidence matrices is presented. The corresponding constructions are applied to known projective planes of order 9. As a result a new description of the Hughes plane of order nine is obtained.
DOI : 10.21136/MB.1995.126096
Classification : 05B25, 51E15
Keywords: ternary; projective plane; incidence matrix; finite projective plane; ternary ring; system of orthogonal Latin squares; Hall plane of order 9; Hughes plane of order 9 
Knoflíček, František. A combinatorial approach to the known projective planes of order nine. Mathematica Bohemica, Tome 120 (1995) no. 4, pp. 347-366. doi: 10.21136/MB.1995.126096
@article{10_21136_MB_1995_126096,
     author = {Knofl{\'\i}\v{c}ek, Franti\v{s}ek},
     title = {A combinatorial approach to the known projective planes of order nine},
     journal = {Mathematica Bohemica},
     pages = {347--366},
     year = {1995},
     volume = {120},
     number = {4},
     doi = {10.21136/MB.1995.126096},
     mrnumber = {1415083},
     zbl = {0847.51005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1995.126096/}
}
TY  - JOUR
AU  - Knoflíček, František
TI  - A combinatorial approach to the known projective planes of order nine
JO  - Mathematica Bohemica
PY  - 1995
SP  - 347
EP  - 366
VL  - 120
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1995.126096/
DO  - 10.21136/MB.1995.126096
LA  - en
ID  - 10_21136_MB_1995_126096
ER  - 
%0 Journal Article
%A Knoflíček, František
%T A combinatorial approach to the known projective planes of order nine
%J Mathematica Bohemica
%D 1995
%P 347-366
%V 120
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1995.126096/
%R 10.21136/MB.1995.126096
%G en
%F 10_21136_MB_1995_126096

[1] Hughes D.R., Piper F.C.: Projective Planes. New York-Heidelberg-Berlin, 1973. | MR | Zbl

[2] Pickert G.: Projektive Eben. Berlin-Göttingen-Heidelberg, 1955.

[3] Stevenson F. W.: Projective Planes. San Francisco, 1972. | MR | Zbl

[4] Paige L. J., Wexler, Ch.: A canonical form for incidence matrices of finite projective planes and their associated Latin squares. Portugaliae Mathematica 12 (1953), 105-112. | MR | Zbl

[5] Hall M.: Projective Planes. Trans. Amer. Math. Soc. 54 (1943), 229-277. | DOI | MR | Zbl

[6] Room T.G., Kirkpatrick P.B.: Miniquaternion Geometry. Cambridge, 1971. | Zbl

[7] Dénes J., Keedwell A.D.: Latin squares and their applications. Budapest, 1974. | MR

[8] Veblen O., Wedderburn J. H. M.: Non-Desargusian and non-Pascalian geometries. Trans. AMS 8 (1907), 379-388. | DOI | MR

[9] Knoflíček F.: On one construction of all quasifields of order 9. Comm. Math. Univ. Carolinae 27 (1986), 683-694. | MR

Cité par Sources :