A NOTE ON THE CONSTRUCTION OF LARGE SET OF LATIN SQUARES WITH ONE ENTRY IN COMMON

Authors

  • CHIN-MEI FU Department of Mathematics, Tamkang University, Tamsui, Taipei Shien, Taiwan, Republic of China.

DOI:

https://doi.org/10.5556/j.tkjm.24.1993.4492

Keywords:

Latin square

Abstract

A latin square of order $n$ is an $n \times n$ array such that each of the integers $1, 2, 3, \cdots, n$ occurs exactly once in each row and each column. A large set of latin squares of order $n$ having only one entry in common is a maximum set of latin squares of order $n$ such that each pair of them contains exactly one fixed entry in common. In this paper, we prove that a large set of latin squares of order $n$ having only one entry in common has $n - 1$ latin squares for each positive integer $n$, $n \ge 4$.

References

J. Denes and A. D. Keedwell, "Latin Squares and their Applications," Academic, London, New York (I974).

Hung-Lin Fu,·"On the construction of certain types of latin squares having prescribed intersections," Ph. D. Thesis, Auburn University, 1980, December.

Hung-Lin Fu, "More results on intersections of latin squares," Journal of Information and Optimization Sciences, Vol II, No. 3 (1990), pp . 525-535.

Show-Ju Hwang, "Large set of latin squares with one entry in common," Master Thesis, Tamkang University, 1991.

Luc Terlinck and C. C. Lindner, "The Construction of Large Sets of Idempotent Quasi.: groups," Eurpoean Journal of Combinatorial theory 9 (1988), pp. 83-89.

Downloads

Published

1993-06-01

How to Cite

FU, C.-M. (1993). A NOTE ON THE CONSTRUCTION OF LARGE SET OF LATIN SQUARES WITH ONE ENTRY IN COMMON. Tamkang Journal of Mathematics, 24(2), 215-220. https://doi.org/10.5556/j.tkjm.24.1993.4492

Issue

Section

Papers

Similar Articles

1 2 3 4 5 6 > >> 

You may also start an advanced similarity search for this article.