Ž . ADVANCES IN APPLIED MATHEMATICS 17, 117121 1996 ARTICLE NO. 0006 Signs on Group Latin Squares Alberto Marini Istituto per le Applicazioni della Matematica e dell’Informatica del CNR, Via A. M. Ampere, 56 I-20131 Milan, Italy ` and Giuseppe Pirillo Istituto per le Applicazioni della Matematica e dell’Informatica del CNR, Viale G. B. Morgagni, 67A I-50134 Florence, Italy Received March 10, 1995 DEDICATED TO THE MEMORY OF ROSA HUANG A simple expression for triples of signs of group Latin squares is given; in particular we prove that it depends onlyon the order. 1. INTRODUCTION We remind the reader that, for n a positive integer, a Latin square of Ž . order n is an n  n matrix whose entries or  alues, or symbols belong to a set X of n elements and such that everyelement of X has exactly one  occurrence in each row and in each column 2. For Latin squares and related notions, we shall use in this paper a  notation compatible with that introduced in 7 . Later we consider canoni - cal Latin squares of order n, i.e., Latin squares whose rows, columns, and ..  4 Ž n. values belong to @ n  0, 1, . . . , n  1 ; let L denote the set of such squares. With an L  L Ž n. one can associate three sequences of permutations; the first is given by its rows L , the second by its columns L and the r ,   , c Ž ... third by matrices of the values L r , c,   @ n ; with the latter we  denote the binary n  n permutation matrix having the entry in the case ² : r , c equal to 1 iff L   . r , c 117 0196-885896 $18.00 Copyright  1996 by Academic Press, Inc. All rights of reproduction in any form reserved.