On dots in boxes or permutation pattern classes and regular languages [10/03/22]
Abstract
This thesis investigates permutation pattern classes in a language theoretic context. Specifically
we explored the regularity of sets of permutations under the rank encoding. We found that the
subsets of plus- and minus-(in)decomposable permutations of a regular pattern class under the
rank encoding are also regular languages under that encoding. Further we investigated the sets of
permutations, which in their block-decomposition have the same simple permutation, and again
we found that these sets of permutations are regular languages under the rank encoding. This
natural progression from plus- and minus-decomposable to simple decomposable permutations led
us further to the set of simple permutations under the rank encoding, which we have also shown
to be regular under the rank encoding. This regular language enables us to nd the set of simple
permutations of any class, independent of whether the class is regular under the rank encoding.
Furthermore the regularity of the languages of some types of classes is discussed. Under the
rank encoding we show that in general the skew-sum of classes, separable classes and wreath classes
are not regular languages; but that the direct-sum of classes, and with some restrictions on the
cardinality of the input classes the skew-sum and wreath sum of classes in fact are regular under
this encoding.
Type
Thesis, PhD Doctor of Philosophy
Rights
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International
http://creativecommons.org/licenses/by-nc-sa/4.0/
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