[seqfan] Re: Given any partition of n into k parts, what's the maximum permutations of parts

[William Keith]

Mr. Pratt:

     I agree that that algorithm will definitely find the optimal value
recursively, and it can be translated to a particular partition.  I am
interested in whether a general form can be established.  If it wouldn't be
too much trouble, could you put up a document somewhere?  Your partition of
512 is implicitly the same as writing the representation of 512 as a sum of
triangular numbers

512 = T(23) + T(16) + T(10) + T(7) + T(4) + T(3) + T(1).

     It seems reasonable that the optimal partition can always be described
this way when the number of parts required is k but n < T(k).  Would you
mind making a list of these T(j) for, say, n up to 100 in the relevant k
region where k < n < T(k) for our perusal?  I wonder if the triangular
numbers that show up for any given n and k might be predictable

Best,
William Keith