A combinatorial approach to the known projective planes of order nine
Mathematica Bohemica (1995)
- Volume: 120, Issue: 4, page 347-366
- ISSN: 0862-7959
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topKnoflíček, František. "A combinatorial approach to the known projective planes of order nine." Mathematica Bohemica 120.4 (1995): 347-366. <http://eudml.org/doc/247798>.
@article{Knoflíček1995,
abstract = {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.},
author = {Knoflíček, František},
journal = {Mathematica Bohemica},
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; ternary; projective plane; incidence matrix},
language = {eng},
number = {4},
pages = {347-366},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A combinatorial approach to the known projective planes of order nine},
url = {http://eudml.org/doc/247798},
volume = {120},
year = {1995},
}
TY - JOUR
AU - Knoflíček, František
TI - A combinatorial approach to the known projective planes of order nine
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 4
SP - 347
EP - 366
AB - 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.
LA - eng
KW - 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; ternary; projective plane; incidence matrix
UR - http://eudml.org/doc/247798
ER -
References
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- Hall M., 10.1090/S0002-9947-1943-0008892-4, Trans. Amer. Math. Soc. 54 (1943), 229-277. (1943) Zbl0060.32209MR0008892DOI10.1090/S0002-9947-1943-0008892-4
- Room T.G., Kirkpatrick P.B., Miniquaternion Geometry, Cambridge, 1971. (1971) Zbl0203.22801
- Dénes J., Keedwell A.D., Latin squares and their applications, Budapest, 1974. (1974) MR0351850
- Veblen O., Wedderburn J. H. M., 10.1090/S0002-9947-1907-1500792-1, Trans. AMS 8 (1907), 379-388. (1907) MR1500792DOI10.1090/S0002-9947-1907-1500792-1
- Knoflíček F., On one construction of all quasifields of order 9, Comm. Math. Univ. Carolinae 27 (1986), 683-694. (1986) MR0874662
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