Jay Pantone

Generating Permutations with Restricted Containers

We investigate a generalization of stacks that we call

The Enumeration of Permutations Avoiding 3124 and 4312

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Staircases, dominoes, and the growth rate of 1324-avoiders

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

Pattern-avoiding involutions: exact and asymptotic enumeration.

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Equipopularity Classes in the Separable Permutations

-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

On isomorphism classes of generalized Fibonacci cubes

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Two examples of unbalanced Wilf-equivalence

-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.

On the Rearrangement Conjecture for Generalized Factor Order Over P

We find the generating function for the class of all permutations that avoid the patterns 3124 and 4312 by showing that it is an inflation of the union of two geometric grid classes.

On the growth of merges and staircases of permutation classes

Abstract We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an upper bound of 13.5. This is done by first finding the precise growth rate of a subclass whose enumeration is related to West-2-stack-sortable permutations, and then combining copies of this subclass in particular ways.