Note: Divisors of the number of Latin rectangles

  • Authors:

  • Douglas S. Stones;Ian M. Wanless

  • Affiliations:

  • School of Mathematical Sciences, Monash University, Vic 3800, Australia;School of Mathematical Sciences, Monash University, Vic 3800, Australia

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2010

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Abstract

A kxn Latin rectangle on the symbols {1,2,...,n} is called reduced if the first row is (1,2,...,n) and the first column is (1,2,...,k)^T. Let R"k","n be the number of reduced kxn Latin rectangles and m=@?n/2@?. We prove several results giving divisors of R"k","n. For example, (k-1)! divides R"k","n when k=