## Systematic Studies in Pattern Avoidance

A Webbook of
Shalosh B. Ekhad,
Lara Pudwell, and
Vince Vatter.

### Introduction:

The concept of pattern avoidance in permutations is a very popular area of research. (See references.)

See Wikipedia: Permutation Pattern for a brief definition and illustration.

While much has been done for the exact enumeration of permutations that avoid a single pattern, less is known about the enumeration of permutations that avoid *sets* of patterns.

With the aid of Vince Vatter's Maple packages FINLABEL and WILFPLUS, along with Doron Zeilberger's Maple package WILF, I have begun to systematically study permutations that avoid multiple patterns. Some of the results contained in this webbook have already been discovered by others, but many are new, and all are completely and rigorously proved by the computer. To our knowledge, this is the largest collection of such results.

- In "Maple Packages", you will find copies of Vince Vatter's and Doron Zeilberger's Maple packages mentioned above, as well as my package "WILFBOOK".
- In "Explanation", you will find a description of the main functions in WILFBOOK so that you can explore these permutations as well.
- In "Output", you will find pdf files with the current permutation data that maple has generated
- In "References", you will find some resources to learn more about pattern avoidance.

Introduction | Maple Packages | Explanation | Output | References

Lara Pudwell -- April 29, 2006