Abstract
In [3] U. Ott introduced a Bruck-Ryser abstract theorem concerning ‘lattices of an R-module’. As one of the applications of this theorem, he obtained a new proof of the Bruck-Ryser theorem for finite projective planes and studied ‘p-curves’ in a projective plane. In this paper, we apply the Bruck-Ryser abstract theorem in order to give a new proof of the Bruck-Ryser-Chowla theorem for symmetric (v, k, λ)-design with (v, k, λ)=1, and to study ‘p-curves’ in arbitrary symmetric designs.
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References
Buratti, M., Metodi Algebrici in Geometria Combinatoria, Ist. Mat. ‘G. Castelnuovo’, Università di Roma ‘La Sapienza’, 1985.
Mordell, J., Diophantine Equations, Academic Press, New York, 1969.
Ott, U., An Elementary Introduction to Algebraic Methods for Finite Projective Planes, Ist. Mat. ‘G. Castelnuovo’, Università di Roma ‘La Sapienza’, 1984.
Ryser, H. J., Combinatorial Mathematics, MAA Carus Math. Monograph 14, John Wiley and Sons distr., 1950.
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Buratti, M. Bruck-Ryser abstract theorem and symmetric designs. Geom Dedicata 27, 241–250 (1988). https://doi.org/10.1007/BF00151357
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DOI: https://doi.org/10.1007/BF00151357