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Computer Search for Large Sets of Idempotent Quasigroups

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Computer Mathematics (ASCM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5081))

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Abstract

A collection of n − 2 idempotent quasigroups of order n is called a large set if any two of them are disjoint, denoted by LIQ(n). While the existence of ordinary LIQ(n) has been extensively studied, the spectrums of large sets of idempotent quasigroups with various identities remain open, for example, large set of Steiner pentagon quasigroups of order 11 which is denoted by LSPQ(11). This paper describes some computer searching efforts seeking to solve such problems. A series of results are obtained, including the non-existence of LSPQ(11).

This work is supported by the National Natural Science Foundation of China (NSFC) under grant No. 60673044.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science Institute of Software, Chinese Academy of Sciences,  

    Feifei Ma & Jian Zhang

  2. Chinese Academy of Sciences, Graduate University,  

    Feifei Ma

Authors
  1. Feifei Ma
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  2. Jian Zhang
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Deepak Kapur

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© 2008 Springer-Verlag Berlin Heidelberg

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Ma, F., Zhang, J. (2008). Computer Search for Large Sets of Idempotent Quasigroups . In: Kapur, D. (eds) Computer Mathematics. ASCM 2007. Lecture Notes in Computer Science(), vol 5081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87827-8_30

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  • DOI: https://doi.org/10.1007/978-3-540-87827-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87826-1

  • Online ISBN: 978-3-540-87827-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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