A Note on Power Sets of Latin Squares

Jezsef Denes1, Gary L. Mulien2, Stephan J. Suchower3
1Csaba Utca 10 v 42 Budapest 1122, Hungary
2Mathematics Department Pennsylvania State University University Park, PA 16802, U.S.A.
3Daniel H. Wagner, Associates Station Square Two Paoli, PA 19301, U.S.A.

Abstract

In this note, we study a group operation on the set of all row-Latin squares of order \(n\) and, as a result, are able to provide a short disproof of the Euler conjecture for infinitely many values of \(n\). We also discuss several related conjectures.