There are N players in a tourney, each plays exactly one match with the others. How can I partition these matches up to K parts to get the most equal partitions if I want to keep the left side of a match present only in one partition, I want matches to be kept sequential and some other properties I try to phrase below.
So basically the set of all matches looks like this: $A=\{(x, y) | x < y, x, y \in [0..N-1]\}$
I have the K subsets $K_i=\{(x, y) | x < y, x, y \in [M_{i-1}..M_i-1]\}, i \in [1..K]$, and would like to know which M series produces the $\min\sum_1^K(|K_i|-\sum_1^K(|K_j|)/K)$ value, assuming $M_0 = 0$.
I can produce the last one, maybe (though I'm not sure it'll be the best solution, but close), because $N*(N-1)/2/K = M_{K}*(M_{K}-1)/2$ gives the value for it after rounding. But is there a non-iterative formula that gives me the whole series of M values?