## Systematic Studies in Pattern Avoidance

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

### Explanation:

**writeBook(L, seql)** -- returns a summary of what FINLABEL and WILF can count for pattern sets with one pattern of each length in L, returns sequences of length seql from WILF

*For example....* writeBook([3], 7) returns:

"This is a systematic study of permutations avoiding ", [3], "pattern sets:"

"There are ", 6, "pattern sets in all"

"They can be trivially divided into", 2, " symmetry classes"

"sorting sets with FINLABEL............"

"sorting sets with WILF (SchemeF)............"

"------------------------------------------------------"

"no symmetry classes were counted by FINLABEL"

"------------------------------------------------------"

"symmetry classes counted with WILF (SchemeF):"

"------------------------------------------------------"

"sequence to ", 7, " terms:", [1, 2, 5, 14, 42, 132, 429]

"symmetry classes with this sequence are: "

{{[1, 3, 2]}, {[2, 1, 3]}, {[2, 3, 1]}, {[3, 1, 2]}}

{{[1, 2, 3]}, {[3, 2, 1]}}

"there are ", 2, " such symmetry classes"

"------------------------------------------------------"

"symmetry classes uncounted by FINLABEL and WILF (SchemeF):"

"there are ", 0, " such symmetry classes"

"------------------------------------------------------"

"summarizing results for ", [3], " pattern sets"

"there are ", 2, " symmetry classes in all"

0, "of them can be counted by FINLABEL"

"that's ", 0., "%"

"of the remaining ones", 2, "of them can be counted by WILF (SchemeF)"

"that's ", 100., "%"

"thus ", 100., "% of the total symmetry classes can be counted by either FINLABEL or WILF (SchemeF)"

**FLprettyprint(L)** -- runs FINLABEL on all L-pattern sets and summarizes results
**Wilfprettyprint(L,seql)** -- runs WILF (SchemeF) on all L-pattern sets and summarizes results with sequences shown up to seql terms

Introduction | Maple Packages | Explanation | Output | References

Lara Pudwell -- April 29, 2006