<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper is one of a series whose goal is to enumerate the avoiders, in the sense of classical pattern avoidance, for each triple of 4-letter patterns. There are 317 symmetry classes of triples of 4-letter patterns, avoiders of 267 of which have already been enumerated. Here we enumerate avoiders for all small Wilf classes that have a representative triple containing the pattern 1342, giving 40 new enumerations and leaving only 13 classes still to be enumerated. In all but one case, we obtain an explicit algebraic generating function that is rational or of degree 2. The remaining one is shown to be algebraic of degree 3. We use standard methods, usually involving detailed consideration of the left to right maxima, and sometimes the initial letters, to obtain an algebraic or functional equation for the generating function.</p></abstract>

This paper is one of a series whose goal is to enumerate the avoiders, in the sense of classical pattern avoidance, for each triple of 4-letter patterns. There are 317 symmetry classes of triples of 4-letter patterns, avoiders of 267 of which have already been enumerated. Here we enumerate avoiders for all small Wilf classes that have a representative triple containing the pattern 1342, giving 40 new enumerations and leaving only 13 classes still to be enumerated. In all but one case, we obtain an explicit algebraic generating function that is rational or of degree 2. The remaining one is shown to be algebraic of degree 3. We use standard methods, usually involving detailed consideration of the left to right maxima, and sometimes the initial letters, to obtain an algebraic or functional equation for the generating function.

Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns"}

This paper is one of a series whose goal is to enumerate the avoiders, in the sense of classical pattern avoidance, for each triple of 4-letter patterns. There...

Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns

Published Online: Aug 06, 2018

Page range: 62 - 97

Received: Aug 03, 2017

DOI: https://doi.org/10.1515/puma-2015-0027

Keywords
pattern avoidance, Wilf-equivalence, generating function, kernel method

© 2018 David Callan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Enumeration of small Wilf classes avoiding 1342 and two other 4-letter patterns

Published Online: Aug 06, 2018

Page range: 62 - 97

Received: Aug 03, 2017

DOI: https://doi.org/10.1515/puma-2015-0027

Keywordspattern avoidance, Wilf-equivalence, generating function, kernel method

© 2018 David Callan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
pattern avoidance, Wilf-equivalence, generating function, kernel method