## 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