[seqfan] Re: next partition into distinct parts

[Alois Heinz]

Here is a Maple program for this problem.  Perhaps someone can
translate it into Mathematica language?

# first partition of n into distinct parts
# with largest part <=i or 0 if not defined
b:= proc(n,i) option remember;
       if n<0 then 0
     elif n=0 then []
     elif i=0 then 0
     elif b(n-i,i-1)<>0 then [i,(b(n-i,i-1)[])]
     elif b(n,  i-1)<>0 then b(n,i-1)
     else 0
       fi
     end:
# next partition into distinct parts
# after given partiton L or 0 if not defined
a:= proc(L) local i, t;
       t:= 0;
       for i from nops(L) to 1 by -1 do
         t:= t+L[i];
         if b(t,L[i]-1)<>0 then
           RETURN ([L[1..i-1][], b(t,L[i]-1)[]])
         fi
       od; 0
     end:
a ([11,4,2]); # gives  [11, 3, 2, 1]

Alois

Am 13.02.2011 07:13, schrieb David Newman:
> Does anyone out there have a Mathematica program which will give the
> next partition into distinct parts?
>
> For example given the partition    {11 , 4 , 2}  as input, it should
> output  {11  ,3  ,2 , 1}.