# Fichier  : Hook 
# Format   : Maple file
# Auteur   : Bruno Gauthier, Institut Gaspard Monge, Universite Marne La Vallee
# A propos : Formule des equerres
# Date     : Mon Apr 23 18:41:52 METDST 1996
###############################################################################

read BijHG;
read BijKratt;




print(`Version of Apr. 23, 1996`):
print(`This is Hook, a Maple program that applies`):
print(`the bijection between column-strict reverse plane partition PL`):
print(`(with entries between 1 and A), a tabloid TL`):
print(`and`):
print(`another tabloid TR`):
print(`such that n(P0) + Wh(TR) = n(PL) + Wc(TL)`):
print(`where P0 is a minimal reverse plane partition`):
lprint(``):
print(`This is a Maple implementation of the proof described in :`):
print(`C. Krattenthaler`):
print(`an involution principle-free bijective proof`):
print(`of Stanley's hook-content formula`):
lprint(``):
print(`The most current version is available on WWW at:`):
print(`http://www-igm.univ-mlv.fr/~gauthier .`):
print(`Please report all bugs to: gauthier@univ-mlv.fr`):
print(`For general help, and a list of the available functions,`):
print(`type "man();". For specific help type "man(procedure_name)"`):
lprint(``):
 
 


 
 
man := proc()

if args=NULL then
print(`Hook  Contains procedures: `):
print(`hillman, grassl, rppTOcrpp, crppTOrpp, hook, kooh`):
print(`For help with a specific procedure, type "man(procedure_name);"`):
 
 
elif nops([args])=1 and op(1,[args])=`hillman` then
print(`hillman(RPP) computes the tabloid T`):
print(`such that n(P)=sum(x,T(x) * h(x))`):
lprint(``):
print(`For example :  hillman([[1, 2, 4], [3, 5, 5], [4]]);`):
print(`gives   [[2, 2, 0], [1, 1, 1], [1]]`):
 

elif nops([args])=1 and op(1,[args])=`grassl` then
print(`grassl(T) computes the reverse plane partition RPP`):
print(`such that n(P)=sum(x,T(x) * h(x))`):
lprint(``):
print(`For example : grassl([[2, 2, 0], [1, 1, 1], [1]]);`):
print(`gives   [[1, 2, 4], [3, 5, 5], [4]])`):


elif nops([args])=1 and op(1,[args])=`rppTOcrpp` then
print(`rppTOcrpp(RPP) computes the tabloid T`):
print(`such that n(P)=sum(x,T(x) * h(x))`):
lprint(``):
print(`For example :  rppTOcrpp([[1,1,3,8], [2,3,4], [5,7,8], [7]],4);`);
print(`gives   [[1, 1, 1, 3], [2, 2, 2], [3, 3, 4], [4]],`);
print(`[[1, 0, 1, 0], [1, 0, 0], [3, 1, 0], [1]]`);

elif nops([args])=1 and op(1,[args])=`crppTOrpp` then
print(`crppTOrpp(PL,TL,A) computes the reverse plane partition RPP`):
print(`such that n(P)=sum(x,T(x) * h(x))`):
lprint(``):
print(`For example :  crppTOrpp([[1,1,1,3], [2,2,2], [3,3,4], [4]], [[1,0,1,0], [1,0,0], [3,1,0],[1]],4);`);
print(`gives   [[1, 1, 3, 8], [2, 3, 4], [5, 7, 8], [7]]`);


elif nops([args])=1 and op(1,[args])=`hook` then
print(`hook(PL,TL,A) computes the tabloid TR`):
print(`such that n(P0) + Wh(TR) = n(PL) + Wc(TL)`):
lprint(``):
print(`For example :  hook([[1,1,3],[2,2,4],[4]], [[2,1,0],[2,0,0],[0]], 4);`):
print(`gives   [[2, 2, 0], [1, 1, 1], [1]]`):
 

elif nops([args])=1 and op(1,[args])=`kooh` then
print(`kooh(TR,A) computes the reverse plane partition PL and the tabloid TL`):
print(`such that n(P0) + Wh(TR) = n(PL) + Wc(TL)`):
lprint(``):
print(`For example : kooh([[2, 2, 0], [1, 1, 1], [1]],4);`):
print(`gives   [[1, 1, 3], [2, 2, 4], [4]], [[2, 1, 0], [2, 0, 0], [0]]`):

else ERROR(`There is no procedure in the Hook program by the name of`,args):
fi:

end:






ajout := proc(T)
# addition de la partition plane minimale

local ret,i,j,rows,cols,k,R;

  ret := calcul(T):

  rows := ret[1]:
  cols := ret[2]:

  k := nops(T):
  
  R := T:

  for i from 1 to k
      do 
         for j from 1 to rows[i]
	     do
                 R := subsop( i=subsop(j=i+op(j,op(i,R)), op(i,R)), R):
	     od:
      od:


end:





enlever := proc(T)
# soustraction de la partition plane minimale

local ret,i,j,rows,cols,k,R;

  ret := calcul(T):

  rows := ret[1]:
  cols := ret[2]:

  k := nops(T):
  
  R := T:

  for i from 1 to k
      do 
         for j from 1 to rows[i]
	     do
                 R := subsop( i=subsop(j=op(j,op(i,R))-i, op(i,R)), R):
	     od:
      od:


end:




hook := proc(PL,TL,A)

RETURN(hillman(enlever(crppTOrpp(PL,TL,A)))):
end:




kooh := proc(TR,A)

RETURN(rppTOcrpp(ajout(grassl(TR)),A)):
end: