# Pattern Avoidance in Reverse Double Lists

## TL;DR

This paper studies pattern avoidance in reverse double lists, providing enumeration results for patterns of length up to 4, classifying Wilf classes, and analyzing growth for longer patterns.

## Contribution

It introduces the concept of reverse double lists and fully classifies pattern avoidance for patterns up to length 4, also analyzing growth for longer patterns.

## Key findings

- Enumerated reverse double lists avoiding patterns of length ≤ 4
- Determined Wilf classes for these patterns
- Characterized polynomial growth for patterns of length ≥ 5

## Abstract

In this paper, we consider pattern avoidance in a subset of words on $\{1,1,2,2,\dots,n,n\}$ called reverse double lists. In particular a reverse double list is a word formed by concatenating a permutation with its reversal. We enumerate reverse double lists avoiding any permutation pattern of length at most 4 and completely determine the corresponding Wilf classes. For permutation patterns $\rho$ of length 5 or more, we characterize when the number of $\rho$-avoiding reverse double lists on $n$ letters has polynomial growth. We also determine the number of $1\cdots k$-avoiders of maximum length for any positive integer $k$.

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Source: https://tomesphere.com/paper/1704.08638