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(, 7) returns:

"This is a systematic study of permutations avoiding ", , "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 ", , " 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