Enumerating Set Orbits

Christian Pech () and Sven Reichard ()
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Christian Pech: Ben-Gurion University of the Negev, Department of Mathematics
Sven Reichard: University of Western Australia

A chapter in Algorithmic Algebraic Combinatorics and Gröbner Bases, 2009, pp 137-150 from Springer

Abstract: Summary We describe a practically efficient canonicity test for orbit representatives of permutation group acting on sets. This allows us to perform a wide range of combinatorial searches. We describe an implementation of the algorithm in GAP. We give a few applications, one of which answers a question by De Wispelaere regarding the classification of all two-ovoids in the classical generalized hexagon of order 4.

Keywords: Set-orbits; Orderly generation; Computer algebra package; Spreads; Incidence structures; Fusions of coherent configuration; Steiner triple systems; Generalized quadrangles; Generalized hexagons; Schur rings (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01960-9_4

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DOI: 10.1007/978-3-642-01960-9_4

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