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Designs, Groups and Computing

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Probabilistic Group Theory, Combinatorics, and Computing

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2070))

Abstract

In this chapter we present some applications of groups and computing to the discovery, construction, classification and analysis of combinatorial designs. The focus is on certain block designs and their statistical efficiency measures, and in particular semiLatin squares, which are certain designs with additional block structure and which generalise Latin squares.

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Acknowledgements

I am grateful to Martin Liebeck for his result of Sect. 3.5.1 and for allowing its inclusion in this chapter. I also thank Eamonn O’Brien for his calculations in Magma. The hospitality of the de Brún Centre for Computational Algebra, NUI Galway, during the Fifth de Brún Workshop is gratefully acknowledged.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Leonard H. Soicher

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  1. Leonard H. Soicher
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Correspondence to Leonard H. Soicher .

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Editors and Affiliations

  1. , Department of Mathematics, National University of Ireland, University Road, Galway, 0, Ireland

    Alla Detinko

  2. , Department of Mathematics, National University of Ireland, University Road, Galway, Ireland

    Dane Flannery

  3. , Mathematics, University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Eamonn O'Brien

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Soicher, L.H. (2013). Designs, Groups and Computing. In: Detinko, A., Flannery, D., O'Brien, E. (eds) Probabilistic Group Theory, Combinatorics, and Computing. Lecture Notes in Mathematics, vol 2070. Springer, London. https://doi.org/10.1007/978-1-4471-4814-2_3

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