#classes: Wrapper for computing number of commutation classes; pass a permutation of type B as a list
#Returns number of commutation classes
#Longest element is of the form [-1, -2, ..., -n]
classes:=proc(perm) option remember:
RETURN(classesRecurse(Array(perm), -1, 1)):
end:
#classesRecurse: Recursive procedure for computing number of commutation classes
classesRecurse:=proc(perm, spot, negs) local swaps, i, sums, c, doneany:
sums:=0:
doneany:=0:
for i from spot to ArrayNumElems(perm)-2 do
if i=-1 and perm[1]<0 then
perm[1]:=-perm[1]:
c:=classes(convert(perm, `list`)):
sums:=sums+negs*c+classesRecurse(perm, i+2, -negs):
perm[1]:=-perm[1]:
doneany:=1:
elif i>-1 and perm[i+1]>perm[i+2] then
swaps:=perm[i+1]:
perm[i+1]:=perm[i+2]:
perm[i+2]:=swaps:
c:=classes(convert(perm, `list`)):
sums:=sums+negs*c+classesRecurse(perm, i+2, -negs):
swaps:=perm[i+1]:
perm[i+1]:=perm[i+2]:
perm[i+2]:=swaps:
doneany:=1:
end:
end:
if spot=-1 and doneany=0 then RETURN(1):
else RETURN(sums):
end:
end:
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