Cheyne Homberger

Generating Permutations with Restricted Containers

We investigate a generalization of stacks that we call

On the effective and automatic enumeration of polynomial permutation classes

\mathcal{C}

The minimum Manhattan distance and minimum jump of permutations

-machines. We show how this viewpoint rapidly leads to functional equations for the classes of permutations that

Expected Patterns in Permutation Classes

\mathcal{C}

Pattern-avoiding involutions: exact and asymptotic enumeration.

-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

Counting Fixed-Length Permutation Patterns

\mathcal{C}

Equipopularity Classes in the Separable Permutations

-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.

Prolific permutations and permuted packings : downsets containing many large patterns

We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations of length n which can be obtained by a finite number of block sorting operations (e.g., reversals, block transpositions, cut-and-paste moves).

The Prolific Proportion of Permutations

Let

Deflatability of Permutation Classes

\pi