#Homework by Mike Murr
#OK to post
#hw24

read(`C24.txt`);

#from C22.txt
#AP(Y,i,m):write a procedure that inputs a Standard Young Tableau
#and an integer i between 1 and nops(Y)+1 and inserts the
#entry m at  the end of the i-th row, or if i=nops(Y)+1 make
#a new row with 1 cell occupied with m
AP:=proc(Y,i,m):

if i=nops(Y)+1 then
 RETURN([op(Y),[m]]):
fi:


if i>1 and nops(Y[i])=nops(Y[i-1]) then
  RETURN(FAIL):
fi:

[op(1..i-1,Y),[op(Y[i]),m],op(i+1..nops(Y),Y)]:


end:
#end from C22.txt

#TabPairs(n,m) was created by modifying SYTpairs(n) of George Spahn, from C24.txt

# TabPairs(n,m) outputs all pairs [S,T] where S is a (column-strict) tableau
# with entries from {1,   ,m}, and T is a STANDARD tableau of the SAME shape;


TabPairs:=proc(n,m) local s,L,S,T,i,j:

L:={}:
for s in Pn(n) do:
 S:=TAB(s,m):
 T:=SYT(s):
 L := L union {seq(seq([S[i],T[j]] ,j=1..nops(T)) ,i=1..nops(S))}:
od:
L:
end: