MATHEMATICA BOHEMICA, Vol. 120, No. 4, pp. 347-366, 1995

A combinatorial approach to the known
projective planes of order nine

Frantisek Knoflicek

Frantisek Knoflicek, Department of Mathematics of the Faculty of Mechanical Engineering, Technical University, Technicka 2, 616 69 Brno, Czech Republic

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.

Keywords: finite projective plane, ternary ring, incidence matrix, system of orthogonal Latin squares, Hall plane of order 9, Hughes plane of order 9

Classification (MSC91): 51E15

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