| Title:
|
A combinatorial approach to the known projective planes of order nine (English) |
| Author:
|
Knoflíček, František |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
347-366 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
ternary |
| Keyword:
|
projective plane |
| Keyword:
|
incidence matrix |
| Keyword:
|
finite projective plane |
| Keyword:
|
ternary ring |
| Keyword:
|
system of orthogonal Latin squares |
| Keyword:
|
Hall plane of order 9 |
| Keyword:
|
Hughes plane of order 9 |
| MSC:
|
05B25 |
| MSC:
|
51E15 |
| idZBL:
|
Zbl 0847.51005 |
| idMR:
|
MR1415083 |
| DOI:
|
10.21136/MB.1995.126096 |
| . |
| Date available:
|
2009-09-24T21:12:50Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126096 |
| . |
| Reference:
|
[1] Hughes D.R., Piper F.C.: Projective Planes.New York-Heidelberg-Berlin, 1973. Zbl 0267.50018, MR 0333959 |
| Reference:
|
[2] Pickert G.: Projektive Eben.Berlin-Göttingen-Heidelberg, 1955. |
| Reference:
|
[3] Stevenson F. W.: Projective Planes.San Francisco, 1972. Zbl 0245.50022, MR 0344995 |
| Reference:
|
[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. Zbl 0053.10802, MR 0060448 |
| Reference:
|
[5] Hall M.: Projective Planes.Trans. Amer. Math. Soc. 54 (1943), 229-277. Zbl 0060.32209, MR 0008892, 10.1090/S0002-9947-1943-0008892-4 |
| Reference:
|
[6] Room T.G., Kirkpatrick P.B.: Miniquaternion Geometry.Cambridge, 1971. Zbl 0203.22801 |
| Reference:
|
[7] Dénes J., Keedwell A.D.: Latin squares and their applications.Budapest, 1974. MR 0351850 |
| Reference:
|
[8] Veblen O., Wedderburn J. H. M.: Non-Desargusian and non-Pascalian geometries.Trans. AMS 8 (1907), 379-388. MR 1500792, 10.1090/S0002-9947-1907-1500792-1 |
| Reference:
|
[9] Knoflíček F.: On one construction of all quasifields of order 9.Comm. Math. Univ. Carolinae 27 (1986), 683-694. MR 0874662 |
| . |
