Operations on partitions Partitions Advanced routines 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 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

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