Generating Permutations with Restricted Containers

Authors

Michael H. Albert, University of OtagoFollow
Cheyne Homberger, University of Maryland - Baltimore County
Jay Pantone, Marquette UniversityFollow
Nathaniel Shar, Rutgers University
Vincent Vatter, University of Florida

Document Type

Article

Language

eng

Publication Date

7-2018

Publisher

Elsevier

Source Publication

Journal of Combinatorial Theory, Series A

Source ISSN

0097-3165

Abstract

We investigate a generalization of stacks that we call - machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that -machines generate, and how these systems of functional equations can be iterated and sometimes solved. General results about the rationality, algebraicity, and the existence of Wilfian formulas for some classes generated by -machines are given. We also draw attention to some relatively small permutation classes which, although we can generate thousands of terms of their counting sequences, seem to not have D-finite generating functions.

Comments

Accepted version. Journal of Combinatorial Theory, Series A, Vol. 157 (July 2018): 205-232. DOI. This article is © Elsevier. Used with permission.

Jay Pantone was affiliated with Dartmouth College at the time of publication.

Recommended Citation

Albert, Michael H.; Homberger, Cheyne; Pantone, Jay; Shar, Nathaniel; and Vatter, Vincent, "Generating Permutations with Restricted Containers" (2018). Mathematical and Statistical Science Faculty Research and Publications. 7.
https://epublications.marquette.edu/math_fac/7