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Permutation Pattern Classes

Version 2.0

August 2015

Michael Albert
Email: malbert at

Steve Linton
Email: sl4 at

Ruth Hoffmann
Email: rh347 at


The PatternClass package is build on the idea of token passing networks building permutation pattern classes. Those classes are best determined by their basis. Both sets can be encoded by rank encoding their permutations. Each, the class and its basis, in their encoded form build a rational language [AAR03]. Rational languages can be easily computed by using automata, which also can be build directly from the token passing networks [ALTd.]. Both ways will build the same language, i.e. the same automaton.


© 2011 by Michael Albert, Steve Linton and Ruth Hoffmann


1 Introduction
2 Token Passing Networks
3 Permutation Encoding
4 From Networks to Automata
5 From Automata to Networks
6 Pattern Classes
7 Some Permutation Essentials
8 Properties of Permutations
9 Regular Languages of Sets of Permutations
10 Miscellaneous functions

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