#OK to post
#Yuxuan Yang, April 2nd, Assignment 18

with(combinat):

Aigner:=proc(n) local i,j,k,m,L,CD,new,tem,set1:
L:=[seq(choose(n,i),i=0..n)]:
CD:=[]:
while nops(CD)<binomial(n,trunc(n/2)) do
 for k from 1 while nops(L[k])=0 do
 od:
new:=[L[k][1]]:
L[k]:=[op(2..nops(L[k]),L[k])]:
 for m from k+1 while m<=n+1 and nops(L[m])>0 do
  tem:=0:
  for set1 in L[m] while tem=0 do
   if nops(convert(new[-1],`set`) minus convert(set1,`set`))=0 then
    tem=1:
    new:=[op(new),set1]:
    L[m]:=convert(convert(L[m],`set`) minus {set1},`list`):
   fi:
  od:
 od:
CD:=[op(CD),new]:
od:
end:

SCD:=proc(n) local i,ind,new,ch,ch1,ch2,se:
if n=0 then 
RETURN([[[]]]):
fi:
if n=1 then 
RETURN([[[],[1]]]):
fi:
ind:=SCD(n-1):
new:=[]:
for ch in ind do 
 ch1:=[op(ch),[op(ch[-1]),n]]:
 if nops(ch1)<>0 then
 new:=[op(new),ch1]:
 fi:
od:

for ch in ind do 
 ch2:=[]:
 for i from 1 to nops(ch)-1 do
  ch2:=[op(ch2),[op(ch[i]),n]]:
 od:
 if nops(ch2)<>0 then 
 new:=[op(new),ch2]:
 fi:
od:
new:
end:


#seq(evalb(convert(SCD(a), set) = convert(Aigner(a), set)), a = 1 .. 10)
#verified outputs.