Systematic Studies in Pattern Avoidance

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


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.

Introduction | Maple Packages | Explanation | Output | References
Lara Pudwell -- April 29, 2006