Abstract
In this paper Cayley’s configurations in projective r-limensional space are re-defined recursively using a combinatorial characterization of them and a recovery algorithm for a generating point set. Then, the loubletriple notation system characterization is justified also through an ad hoc algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bokowsky, J. and Sturmnfels, B. (1989) Computational Synthetic Geometry, LNM, vol. 1355. Springer-Verlag.
Brieskorn, E. and Knörrer, H. (1989) Plane Algebraic Curves, Birkhäuser.
Cárdenas, H. and San Agustín, R. (1994) On Veronese’s decomposition Theorem and the geometry of the outer autonorphism of S6, Publicaciones prelininares del Instituto de Matenáticas, U.N.A.M., vol.35.
Cárdenas, H. and San Agu Stín, R. (1994) On Cayley’s construction and certain combinatorial Designs, Preprint.
Carmichael, R.D. (1956) Introduction to the theory of groups of finite order. Dover Publications, Inc.
Cayley, A. (1864), J. f. Reine u. Angewandte math., vol. 31, p. 213 et seq.
Cremona, L. (1877) Teoremi stereornetrici, dai quali si deducono le proprietá dell’ esagramno di Pascal, Menoria dei Reale Academie dei Lincei, vol. I, pp. 854–874.
Henderson, A. (1911) The 27 lines upon a cubic surface. Heffner Publishing Co., New York.
Hilbert D. and Cohn-Vossen, S. (1952) Geometry and the Imagination. Chelsea Publishing Co.
Salmon, G. (1952) A treatise on Conic Sections, Chelsea, , pp. 219–236.
San Agustín, R. (1993) Configuraciones de rectas en el espacio, UAM-I monograph nun. 04.0406.II.01.11.92. México.
Steinitz, E. (1910) Konfigurationen der projectiven geometrie. Enc.yklop. d. nath. Wissensch., vol. III, 1, pp. 481–516, Berlin.
Veronese, G. (1877) Nuovi Teoreni sull Hexagramum Misticum, Memorie dei Reale Academie dei Lincei, vol. I, pp. 649–703.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Agustin, R.S. (1995). On Cayley’s Projective Configurations an Algorithmic Study. In: White, N.L. (eds) Invariant Methods in Discrete and Computational Geometry. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8402-9_14
Download citation
DOI: https://doi.org/10.1007/978-94-015-8402-9_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4572-0
Online ISBN: 978-94-015-8402-9
eBook Packages: Springer Book Archive