# Generating Permutations with Restricted Containers

with
Michael Albert,
Jay Pantone,
Nathaniel Shar, and
Vince Vatter

## Abstract:

We investigate a generalization of stacks that we call $\C$-machines. We show
how this viewpoint rapidly leads to functional equations for the classes of
permutations that $\C$-machines generate, and how these systems of functional
equations can frequently be solved by either the kernel method or, much more
easily, by guessing and checking. General results about the rationality,
algebraicity, and the existence of Wilfian formulas for some classes generated
by $\C$-machines are given. We also draw attention to some relatively small
permutation classes which, although we can generate thousands of terms of their
enumerations, seem to not have D-finite generating functions.