# 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} }

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…

## 18 Citations

On the Number of Conjugate Classes of Derangements

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The number of conjugate classes of derangements of order
n
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of the restricted partitions with every portion greater than 1. It is also equal to the…

Bounds on the number of autotopisms and subsquares of a Latin square

- MathematicsComb.
- 2013

It is shown that an n×n Latin square has at most nO(log k) subsquares of order k and admits at mostN(log n) autotopisms and the theorem by McKay and Wanless that gave a factorial divisor of Rn is extended.

The Many Formulae for the Number of Latin Rectangles

- MathematicsElectron. J. Comb.
- 2010

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 Computing the Number of Latin Rectangles

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- 2016

A formal proof of Doyle’s formula for arbitrary k is given and some research problems and conjectures about the divisors of Lk,n are presented.

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This document is a collection of comments that I wrote down while reading the first four chapters of the book "Discrete Groups, Expanding Graphs and Invariant Measures" by Alexander Lubotzky. Most of…

EIGENVALUES AND EIGENVECTORS OF LATIN SQUARES IN MAX-PLUS ALGEBRA

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- 2014

A Latin square of order n is a square matrix with n diﬀerent numberssuch that numbers in each column and each row are distinct. Max-plus Algebra isalgebra that uses two operations, ⊕ and ⊗. In this…

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