Skip to main content Accessibility help
×
Home

Integral powers of order three Latin square matrices

  • N. Gauthier (a1)

Extract

An order-n Latin square contains numbers, each of which is one of a set of n real numbers, , arranged in the form of an n × n matrix, in such a way that each row and each column of the matrix contains all n numbers. Euler (1707-1783) was the first to study the properties of Latin squares and they have been the focus of continued attention since. Studies of Latin squares naturally lead one to elements of group theory and of matrix theory. As will be shown in this note, both of these features may offer interesting investigative opportunities for classroom discussions of the permutation group on three symbols and of the algebra of the associated permutation matrices.

Copyright

References

Hide All
1. Emanouilidis, E., Powers of Latin squares, Math. Gaz. 90 (November 2006) pp. 478481.
2. Emanouilidis, E. and Bell, R., Latin squares and their inverses, Math. Gaz. 88 (March 2004) pp. 127128.
3. Trenkler, G. and Trenkler, D., On singular 3x3 semi-diagonal Latin squares, Math. Gaz. 91 (March 2007) pp. 126128.
4. Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, Dover Publications, New York (1972), 9th printing, p. 823, sections 24.1.1 (binomial expansion) and 24.1.2 (multinomial expansion).
5. Dixon, J. D. and Mortimer, B., Permutation Groups, Springer-Verlag, New York (1996).
6. Goodman, R. and Wallach, N. R., Representations and Invariants of the Classical Groups, in Rota, G.-C. (ed.), Encyclopedia of mathematics and its applications, vol. 68. Cambridge University Press, Cambridge (1998), section 2.5.
7. Banchoff, T. and Wermer, J., Linear algebra through geometry, Springer-Verlag, New York (1983), pp. 141144.

Integral powers of order three Latin square matrices

  • N. Gauthier (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed