Abstract
Some remarks on 103-configurations which contain the complete graph K 4 are given, on their representations, and on projective realizability. Results are applied to show a class of configurations that cannot be realized in any Pappian projective space.
Similar content being viewed by others
References
Betten D., Schumacher U.: The ten configurations 103. Rostock. Math. Kolloq. 46, 3–10 (1993)
Coxeter H.S.M.: Desargues configurations and their collineation groups. Math. Proc. Camb. Phil. Soc. 78, 227–246 (1975)
Gorodowienko J., Prażmowska M., Prażmowski K.: Elementary characterizations of some classes of reducts of affine spaces J. Geom. (to appear). doi:10.1007/s00022-008-2056-6.
Gropp H.: Configurations and their realization, Combinatorics (Rome and Montesilvano, 1994). Discrete Math. 174(1–3), 137–151 (1997)
Hilbert D., Cohn-Vossen P.: Anschauliche Geometrie. Springer Verlag, Berlin (1932). (English translation: Geometry and the Imagination, AMS Chelsea Publishing).
Jankowska B., Prażmowska M., Prażmowski K.: Line graphs, their desarguesian closure, and corresponding groups of automorphisms. Demonstratio Math. 40(4), 971–986 (2007)
Lanman K.T.: The taxonomy of various combinatoric and geometric configurations. In: Proceedings of the 2001 Butler University Undergraduate Research Conference. Holcomb Research Institute.
Petelczyc K.: Series of inscribed n-gons and rank 3 configurations. Beiträge Algebra Geom. 46(1), 283–300 (2005)
Petelczyc K., Prażmowski K.: Multiplied configurations, series induced by correlations. Results Math. 49, 313–337 (2006)
Polster B.: A Geometrical Picture Book. Springer Verlag, New York (1998)
Prażmowska M.: Multiple perspective and generalizations of the Desargues configuration. Demonstratio Math. 39(4), 887–906 (2006)
Prażmowska M., Prażmowski K.: Some generalization of Desargues and Veronese configurations. Serdica Math. J. 32(2–3), 185–208 (2006)
Prażmowska M., Prażmowski K.: Combinatorial Veronese structures, their geometry, and problems on embeddability. Results Math. 51, 275–308 (2008)
van Maldeghem H.: Slim and bislim geometries. In: Topics in Diagram Geometry, pp. 227–254. Quad. Mat. 12, Dept. Math., Seconda Univ. Napoli, Caserta (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by D. Ghinelli.
Rights and permissions
About this article
Cite this article
Petelczyc, K., Prażmowska, M. 103-configurations and projective realizability of multiplied configurations. Des. Codes Cryptogr. 51, 45–54 (2009). https://doi.org/10.1007/s10623-008-9242-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-008-9242-2