ON THE NUMBER OF LATIN RECTANGLES

@article{Stones2010ONTN,
  title={ON THE NUMBER OF LATIN RECTANGLES},
  author={Douglas S. Stones},
  journal={Bulletin of the Australian Mathematical Society},
  year={2010},
  volume={82},
  pages={167 - 170}
}
  • Douglas S. Stones
  • Published 22 June 2010
  • Mathematics
  • Bulletin of the Australian Mathematical Society
This thesis primarily investigates the number Rk,n of reduced k X n Latin rectangles. Specifically, we find many congruences that involve Rk,n with the aim of improving our understanding of Rk,n. In general, the problem of finding Rk,n is difficult and furthermore, the literature contains many published errors. Modern enumeration algorithms, such as that of McKay and Wanless, require lengthy computations and storage of a large amount of data. Consequently, even into the future, the possibility… 
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References

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Abstract.We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order 11, (2) answer some questions of Alter by showing that
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How not to prove the Alon-Tarsi conjecture
Abstract The sign of a Latin square is −1 if it has an odd number of rows and columns that are odd permutations; otherwise, it is +1. Let LE n and Lo n be, respectively, the number of Latin squares
The Many Formulae for the Number of Latin Rectangles
TLDR
The method of Sade in finding $L_{7,7}$, an important milestone in the enumeration of Latin squares, but which was privately published in French, is described in detail.
On the Number of Even and Odd Latin Squares of Orderp+1
Abstract It is shown that given an odd primep, the number of even latin squares of orderp+1 is not equal to the number of odd latin squares of orderp+1. This result is a special case of a conjecture
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Latin Squares and Their Applications Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the
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