The Distributions of the Entries of Young Tableaux
The Distributions of the Entries of Young Tableaux
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青年剧作品分布
DOI：
10.1006/jcta.2001.3200
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
H. Wilf
中科院分区：
文献类型：
--
作者：
B. McKay;J. Morse;H. Wilf
设T是一个标准的杨氏形状表？？K.我们证明，随机选择的n个单元的Young表包含T作为子表的概率是，在极限n？∞，等于f？/ k！，在哪里f？是所有形状的场景的数量？换句话说，一个大的画面包含T的概率等于形状为T的画面的数量除以k！。我们给出了几个应用程序，一组规定的条目将出现在一组规定的单元格的一个画面的概率，并给出的形状subtableaux将发生的概率。我们的论点依赖于一个概念的准随机性的家庭的排列，我们给出了充分的条件，这举行。
Let T be a standard Young tableau of shape ??k. We show that the probability that a randomly chosen Young tableau of n cells contains T as a subtableau is, in the limit n?∞, equal to f?/k!, where f? is the number of all tableaux of shape ?. In other words, the probability that a large tableau contains T is equal to the number of tableaux whose shape is that of T, divided by k!. We give several applications, to the probabilities that a set of prescribed entries will appear in a set of prescribed cells of a tableau, and to the probabilities that subtableaux of given shapes will occur. Our argument rests on a notion of quasirandomness of families of permutations, and we give sufficient conditions for this to hold.