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4 results

  • MAXIMUM GENUS EMBEDDINGS OF LATIN SQUARES

  • Part of
  • TERRY S. GRIGGS, CONSTANTINOS PSOMAS, JOZEF ŠIRÁŇ
  • Journal:
    Glasgow Mathematical Journal / Volume 60 / Issue 2 / May 2018
    Published online by Cambridge University Press:
    30 October 2017, pp. 495-504
    Print publication:
    May 2018
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  • It is proved that every non-trivial Latin square has an upper embedding in a non-orientable surface and every Latin square of odd order has an upper embedding in an orientable surface. In the latter case, detailed results about the possible automorphisms and their actions are also obtained.

  • Distributive and Anti-distributive Mendelsohn Triple Systems

  • Diane M. Donovan, Terry S. Griggs, Thomas A. McCourt, Jakub Opršal, David Stanovský
  • Journal:
    Canadian Mathematical Bulletin / Volume 59 / Issue 1 / 01 March 2016
    Published online by Cambridge University Press:
    20 November 2018, pp. 36-49
    Print publication:
    01 March 2016
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  • We prove that the existence spectrum of Mendelsohn triple systems whose associated quasigroups satisfy distributivity corresponds to the Loeschian numbers, and provide some enumeration results. We do this by considering a description of the quasigroups in terms of commutative Moufang loops. In addition we provide constructions of Mendelsohn quasigroups that fail distributivity for asmany combinations of elements as possible. These systems are analogues of Hall triple systems and anti-mitre Steiner triple systems respectively.