An $n imes n$ array is emph{avoidable} if for each set of $n$ symbols there is a Latin square on these symbols which differs from the array in every cell. We characterise all unavoidable square arrays with at most 2 symbols, and all unavoidable arrays of order at most 4. We also identify a number of general families of unavoidable arrays, which we conjecture to be a complete account of unavoidable arrays. Next, we investigate arrays with multiple entries in each cell, and identify a number of families of unavoidable multiple entry arrays. We also discuss fractional Latin squares, and their connections to unavoidable arrays. We note that when rephrasing our results as edge list-colourings of complete bipartite graphs, we have a situation where the lists of available colours are shorter than the length guaranteed by Galvin's theorem to allow proper colourings.
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机译：$ n times n $数组是 emph {evervable}如果为每组$ n $符号，这些符号上有一个拉丁广场，而来自每个单元格中的数组不同。我们以最多2个符号的所有不可避免的方形阵列为特征，以及最多的所有不可避免的订单数目。我们还确定了许多不可避免的阵列的一般家庭，我们猜想是不可避免的阵列的完整叙述。接下来，我们在每个单元格中调查具有多个条目的阵列，并识别多个不可避免的多个条目阵列的许多系列。我们还讨论了分数拉丁方块及其与不可避免的阵列的连接。我们注意到将我们的结果作为完整二角形图的边缘列表彩色重新描述，我们有一个情况，可用颜色的列表短于Galvin定理保证的长度，以允许适当的着色。
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