Open AccessA NOTE ON THE CONSTRUCTION OF LARGE SET OF LATIN SQUARES WITH ONE ENTRY IN COMMON
Author(s) -
Chin-Mei Fu
Publication year - 1993
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.24.1993.4492
Subject(s) - latin square , mathematics , integer (computer science) , combinatorics , order (exchange) , set (abstract data type) , least squares function approximation , square (algebra) , discrete mathematics , statistics , computer science , geometry , chemistry , rumen , food science , finance , estimator , fermentation , economics , programming language
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 $n$, $n \ge 4$.