Discrepancy in different numbers of colors

In this article, we investigate the interrelation between the discrepancies of a given hypergraph in different numbers of colors. Being an extreme example we determine the multi-color discrepancies of the k-balanced hypergraph on partition classes of (equal) size n. Let . Set k₀ k mod c and b_nkc (n?n/c/k)k/c. For the discrepancy in c colors we show

if k₀≠0, and , if c divides k. This shows that, in general, there is little correlation between the discrepancies of in different numbers of colors. If c divides k though, holds for any hypergraph .