Simple permutations and pattern restricted permutations |
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Authors: | MH Albert MD Atkinson |
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Institution: | Department of Computer Science, University of Otago, Dunedin, New Zealand |
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Abstract: | 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. |
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Keywords: | Permutation Enumeration Pattern-restricted |
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