Rationality for subclasses of 321-avoiding permutations

Albert, Michael; Brignall, Robert; Ruskuc, Nik and Vatter, Vincent (2019). Rationality for subclasses of 321-avoiding permutations. European Journal of Combinatorics, 78 pp. 44–72.

DOI: https://doi.org/10.1016/j.ejc.2019.01.001

Abstract

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.

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About

• Item ORO ID
• 59056
• Item Type
• Journal Item
• ISSN
• 0195-6698
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2019 Elsevier
• Depositing User
• Robert Brignall