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3 results

  • THERE ARE ASYMPTOTICALLY THE SAME NUMBER OF LATIN SQUARES OF EACH PARITY

  • Part of
  • NICHOLAS J. CAVENAGH, IAN M. WANLESS
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 94 / Issue 2 / October 2016
    Published online by Cambridge University Press:
    21 July 2016, pp. 187-194
    Print publication:
    October 2016
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  • A Latin square is reduced if its first row and first column are in natural order. For Latin squares of a particular order $n$, there are four possible different parities. We confirm a conjecture of Stones and Wanless by showing asymptotic equality between the numbers of reduced Latin squares of each possible parity as the order $n\rightarrow \infty$.

  • A study of the representations supported by the orbit closure of the determinant

  • Part of
  • Shrawan Kumar
  • Journal:
    Compositio Mathematica / Volume 151 / Issue 2 / February 2015
    Published online by Cambridge University Press:
    24 October 2014, pp. 292-312
    Print publication:
    February 2015
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  • We show the existence of a large family of representations supported by the orbit closure of the determinant. However, the validity of our result is based on the validity of the celebrated ‘Latin square conjecture’ due to Alon and Tarsi or, more precisely, on the validity of an equivalent ‘column Latin square conjecture’ due to Huang and Rota.