Siamese combinatorial objects via computer algebra experimentation

Mikhail Klin; Sven Reichard; Andrew Woldar

doi:10.1007/978-3-642-01960-9_2

Siamese combinatorial objects via computer algebra experimentation

Mikhail Klin, Sven Reichard, Andrew Woldar

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

4 Scopus citations

Abstract

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,q²) 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.

Original language	English
Title of host publication	Algorithmic Algebraic Combinatorics and Gröbner Bases
Publisher	Springer Berlin Heidelberg
Pages	67-112
Number of pages	46
ISBN (Print)	9783642019593
DOIs	https://doi.org/10.1007/978-3-642-01960-9_2
State	Published - 1 Dec 2009

Keywords

Association scheme
Coherent configuration
Color graph
Computer algebra package
Distance regular graph
Generalized quadrangle
Siamese Steiner design
Siamese association scheme
Siamese color graph
Spread
Steiner system
Strongly regular graph

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.1007/978-3-642-01960-9_2

Cite this

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abstract = "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,q2) 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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AU - Reichard, Sven

AU - Woldar, Andrew

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N2 - 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,q2) 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.

AB - 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,q2) 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.

KW - Association scheme

KW - Coherent configuration

KW - Color graph

KW - Computer algebra package

KW - Distance regular graph

KW - Generalized quadrangle

KW - Siamese Steiner design

KW - Siamese association scheme

KW - Siamese color graph

KW - Spread

KW - Steiner system

KW - Strongly regular graph

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BT - Algorithmic Algebraic Combinatorics and Gröbner Bases

PB - Springer Berlin Heidelberg

ER -

Siamese combinatorial objects via computer algebra experimentation

Abstract

Keywords

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