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Algorithmic Algebraic Combinatorics and Gröbner Bases pp 67–112Cite as

Siamese Combinatorial Objects via Computer Algebra Experimentation

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Following Kharaghani and Torabi [On a decomposition of complete graphs, Graphs Comb., 19 (2003), 519–526], we introduce new concepts of Siamese color graph, Siamese association scheme and Siamese Steiner design. With the aid of a computer, we determine all Siamese objects on 15 points, as well as hundreds on 40 points. As a generalization of accumulated observations, an infinite series of Siamese association schemes related to certain imprimitive actions of the groups PSL(2,q 2) is outlined. Special attention is paid to the spirit of computer-aided activity, namely to algorithms, technical data, successful ad hoc tricks, and computer-free interpretations of obtained results.

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Author information

Authors and Affiliations

  1. Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel

    Mikhail Klin

  2. University of Western Australia, Crawley, 6009, Western Australia

    Sven Reichard

  3. Villanova University, Villanova, PA, 19085, USA

    Andrew Woldar

Authors
  1. Mikhail Klin
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  2. Sven Reichard
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  3. Andrew Woldar
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Correspondence to Mikhail Klin .

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Editors and Affiliations

  1. Department of Mathematics, Ben-Gurion University of the Negev, POB 653, 84633, Beer Sheva, Israel

    Mikhail Klin

  2. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    Gareth A. Jones

  3. Faculty of Computer Science, Laboratory for Cryptography and Computer Security, Tržaška cesta 25, 1000, Ljubljana, Slovenia

    Aleksandar Jurišić

  4. Department of Mathematics and Computer Science, Netanya Academic College, University st. 1, 42 365, Netanya, Israel

    Mikhail Muzychuk

  5. V.A. Steklov Mathematical Institute, Laboratory of Representation Theory and Computational Mathematics, Fontanka 27, 191023, St. Petersburg, Russia

    Ilia Ponomarenko

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Klin, M., Reichard, S., Woldar, A. (2009). Siamese Combinatorial Objects via Computer Algebra Experimentation. In: Klin, M., Jones, G.A., Jurišić, A., Muzychuk, M., Ponomarenko, I. (eds) Algorithmic Algebraic Combinatorics and Gröbner Bases. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01960-9_2

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