Elsevier

Discrete Mathematics

Volume 300, Issues 1–3, 6 September 2005, Pages 1-15
Discrete Mathematics

Simple permutations and pattern restricted permutations

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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.

Keywords

Permutation
Enumeration
Pattern-restricted

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