Help:=proc(): print(`Fn(n,q), Fni(n,i,q), Gn(n,q), Gni(n,i,q),`): 
print(`Gnji(n,j,i,q)`):
end:


#Fn(n,q): the generating function according to inv of S_n

Fn:=proc(n,q) local i: option remember:

if n=0 then RETURN(1): fi:

add(Fni(n,i,q),i=1..n):
end:

#Fni(n,i,q): the gen. fun. according to inv of the
#set of prems on {1, ..., n} that end in i
Fni:=proc(n,i,q) option remember:
if n<0 then ERROR(`Bad input`): fi:

sort(expand(q^(n-i)*Fn(n-1,q))):
end:



#Gn(n,q): the generating function according to maj of S_n

Gn:=proc(n,q) local i: option remember:

if n=0 then RETURN(1): fi:

add(Gni(n,i,q),i=1..n):
end:

#Gni(n,i,q): the gen. fun. according to maj of the
#set of prems on {1, ..., n} that end in i
Gni:=proc(n,i,q) option remember:
if n<0 then ERROR(`Bad input`): fi:
add(Gnji(n,j,i,q),j=1..i-1)+add(Gnji(n,j,i,q),j=i+1..n):

end:


Gnji:=proc(n,j,i,q) option remember:


end: