<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper basically completes a project to enumerate permutations avoiding a triple <italic>T</italic> of 4-letter patterns, in the sense of classical pattern avoidance, for every <italic>T</italic>. There are 317 symmetry classes of such triples <italic>T</italic> and previous papers have enumerated avoiders for all but 14 of them. One of these 14 is conjectured not to have an algebraic generating function. Here, we find the generating function for each of the remaining 13, and it is algebraic in each case.</p></abstract>

This paper basically completes a project to enumerate permutations avoiding a triple T of 4-letter patterns, in the sense of classical pattern avoidance, for every T. There are 317 symmetry classes of such triples T and previous papers have enumerated avoiders for all but 14 of them. One of these 14 is conjectured not to have an algebraic generating function. Here, we find the generating function for each of the remaining 13, and it is algebraic in each case.

Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done

Pure Mathematics and Applications

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

This paper basically completes a project to enumerate permutations avoiding a triple T of 4-letter patterns, in the sense of classical pattern avoidance, for...

Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done

Published Online: Nov 01, 2019

Page range: 14 - 69

Received: Jan 19, 2018

Accepted: May 16, 2018

DOI: https://doi.org/10.1515/puma-2015-0031

Keywords
pattern avoidance, Wilf-equivalence, generating function, INSENC algorithm

© 2019 David Callan et al., published by Sciendo

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

Enumeration of permutations avoiding a triple of 4-letter patterns is almost all done

Published Online: Nov 01, 2019

Page range: 14 - 69

Received: Jan 19, 2018

Accepted: May 16, 2018

DOI: https://doi.org/10.1515/puma-2015-0031

Keywordspattern avoidance, Wilf-equivalence, generating function, INSENC algorithm

© 2019 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, INSENC algorithm