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Latin Squares with Prescribed Diagonals

Published online by Cambridge University Press:  20 November 2018

A. J. W. Hilton  and
C. A. Rodger
A. J. W. Hilton
Affiliation:
University of Reading, Reading, England
C. A. Rodger
Affiliation:
University of Reading, Reading, England
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1. Introduction. An incomplete latin rectangle on t symbols σ1 …, σt of size r × s is an r × s matrix in which each cell is occupied by exactly one of the symbols σ1 …, σt in such a way that no symbol occurs more than once in any row or more than once in any column. If r = t or s = t then it is a latin rectangle; if r = s < t it is an incomplete latin square; if r = s = t it is a latin square. The diagonal of a latin square consists of the cells (i, i) (1 ≦ i ≦ t) together with the symbols occupying those cells. Let an allowed sequence of length t be a sequence of length t in which no symbol occurs exactly t – 1 times. Let an allowed diagonal of length t be a diagonal occupied by an allowed sequence.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 6 , 01 December 1982 , pp. 1251 - 1254
Copyright
Copyright © Canadian Mathematical Society 1982

References

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