Latin squares with forbidden entries (Q2500966)

Summary: An \(n \times n\) array is avoidable if there exists a Latin square which differs from the array in every cell. The main aim of this paper is to present a generalization of a result of \textit{A. G. Chetwynd} and \textit{S. J. Rhodes} [J. Graph Theory 25, No.~4, 257--266 (1997; Zbl 0878.05018)] involving avoiding arrays with multiple entries in each cell. They proved a result regarding arrays with at most two entries in each cell, and we generalize their method to obtain a similar result for arrays with arbitrarily many entries per cell. In particular, we prove that if \(m\in {\mathbb N}\), there exists an \(N=N(m)\) such that if \(F\) is an \(N\times N\) array with at most \(m\) entries in each cell, then \(F\) is avoidable.