Discrepancy in different numbers of colors Original Research Article

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 Hnk on partition classes of (equal) size n. Let c,k,n∈N. Set k0 ≔ k mod c and bnkc ≔ (n−⌊n/⌈c/k⌉⌋)k/c. For the discrepancy in c colors we showbnk0c⩽disc(Hnk,c)