SYMMETRICA-MANUAL -- Comparing partitions

Comparing partitions

Comparing partitions

There are several orders on sets of partitions. The standard routine comp() uses the lexicographic order, which means: you compare the first entries of the partition sequences in question first, then you compare the second entries, and so on. There is another order, the so-called dominance order, it is checked by the following routine

NAME: dom_comp_part
SYNOPSIS: INT dom_comp_part(OP parta, partb)
DESCRIPTION: compares two partitions according to the dominance order. At the moment only for the VECTOR representation.
RETURN: 0 if the partitions in question are equal, and 1 if parta is bigger then partb, and -1 if parta is smaller then partb, any other other value means that parta and partb are incompatible.

Look at the following example:

Example:

...
scan(INTEGER,a);
makevectorofpart(a,b); println(b);
m_ilih_m(S_V_LI(b),S_V_LI(b),c);
for (i=0L;i<S_V_LI(b);i++)
   for (j=0L;j<S_V_LI(b);j++)
      m_i_i(dom_comp_part(S_V_I(b,i),S_V_I(b,j)),S_M_IJ(c,i,j));
println(c);
...

It prints the matrix c of the results of the comparison of all partitions of the weight a.

harald.fripertinger "at" uni-graz.at, May 26, 2011

Comparing partitions