read `DyckClever.txt`:

with(combinat):

N:=5:

S:=powerset({seq(i,i=1..N)}):

print(` Given sets A and B of positive integersWe are interested in counting the number of Dyck paths `):
print(`whose peak-heights are never in A and valley-heights are never in B`):
print(``):
print(`Below we give the quadratic equations satisfied by the generating function, as well as the expression in terms`):
print(`C=(1-sqrt(1-4*x))/(2*x), the generating function for the Catalan mumbers for all sets A and B that are subsets of`):
print(``):
print({seq(i,i=1..N)}):

for A in S do
for B in S do
print(``):
print(`----------------------------`):
print(``):
 print(`(A,B)= `, (A,B)):
print(``):
 print(fAB(A,B,x,P)=0  ):
print(``):
 print(P= fABcat(A,B,x,C) ):
print(``):
od:
od:


print(``):
print(`-------------------------`):
print(``):
print(`This took`, time(), `second. `):
print(``):
quit: