An n × 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 Chetwynd and Rhodes 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 ∞ N there exists an N = N(m) such that if F is an N × N array with at most m entries in each cell, then F is avoidable.
|Number of pages||9|
|Journal||Electronic Journal of Combinatorics|
|Issue number||1 R|
|State||Published - 12 May 2006|