Simple permutations and pattern restricted permutations
Simple permutations and pattern restricted permutations
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DOI：
10.1016/j.disc.2005.06.016
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发表时间：
2005-09-06
影响因子：
0.8
通讯作者：
Atkinson, MD
中科院分区：
文献类型：
--
作者：
Albert, MH;Atkinson, MD
一个简单的排列是不会将任何非平地间隔映射到一个间隔的排列。结果表明，如果模式限制类排列中的简单排列数是有限的，则该类具有代数生成函数，并且由有限的限制集定义。给出了具有无限数量简单排列的类的一些部分结果。通过相同技术获得的结果示例；特别是表明，在132个避免置换中正确包含的每个模式限制类都具有合理的生成函数。 （c）2005 Elsevier B.V.保留所有权利。
A simple permutation is one that does not map any non-trivial interval onto an interval. It is shown that, if the number of simple permutations in a pattern restricted class of permutations is finite, the class has an algebraic generating function and is defined by a finite set of restrictions. Some partial results on classes with an infinite number of simple permutations are given. Examples of results obtainable by the same techniques are given; in particular it is shown that every pattern restricted class properly contained in the 132-avoiding permutations has a rational generating function. (c) 2005 Elsevier B.V. All rights reserved.