Rationality for subclasses of 321-avoiding permutations
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We prove that every proper subclass of the 321-avoiding permutations that is defined either by only finitely many additional restrictions or is well-quasi-ordered has a rational generating function. To do so we show that any such class is in bijective correspondence with a regular language. The proof makes significant use of formal languages and of a host of encodings, including a new mapping called the panel encoding that maps languages over the infinite alphabet of positive integers avoiding certain subwords to languages over finite alphabets.
Albert , M H , Brignall , R , Ruskuc , N & Vatter , V 2019 , ' Rationality for subclasses of 321-avoiding permutations ' , European Journal of Combinatorics , vol. 78 , pp. 44-72 . https://doi.org/10.1016/j.ejc.2019.01.001
European Journal of Combinatorics
Copyright © 2019 Elsevier Ltd. All rights reserved. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.ejc.2019.01.001
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