## Systematic Studies in Pattern Avoidance

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

### Output:

There are 3 output files, each compiled to varying degrees of completion.

**A general entry in any of the files has the following information (if available):**
- generating function
- sequence to 30 terms (a(i) = the number of permutations of length i avoiding a set of patterns)
- results of searching for sequence in the online encyclopedia of integer sequences
- recurrence formula from Findrec (from the GuessHolo package)
- asymptotic expansion from Asy (from the GuessHolo package)
- asymptotic results of Zinn (from the GuessHolo package)
- number of symmetry classes with this sequence/generating function
- one representative from each symmetry class (or in the case of FLoutput,
*all* pattern sets with this sequence)

**Current output files:**
- FLsummary.pdf -- the most recent file; contains summarized output from both FINLABEL and WILF, with asymptotics computed for everything; however, does not include pattern sets that FINLABEL has studied but WILF has not yet reached
- FLshort2.pdf -- contains a summarized version of all data from FINLABEL
- FLoutput.pdf -- same as FLshort.pdf, but lists all pattern sets instead of one representative from each trivial symmetry class

*note: the above files contain pattern sets which are not closed. in a future version, such degenerate pattern sets will be removed from the output and from the statistics at the end of the file.

Introduction | Maple Packages | Explanation | Output | References

Lara Pudwell -- April 29, 2006