5 research outputs found
Discrepancy of Symmetric Products of Hypergraphs
For a hypergraph , its --fold symmetric
product is . We give
several upper and lower bounds for the -color discrepancy of such products.
In particular, we show that the bound proven for all in [B. Doerr, A. Srivastav, and P.
Wehr, Discrepancy of {C}artesian products of arithmetic progressions, Electron.
J. Combin. 11(2004), Research Paper 5, 16 pp.] cannot be extended to more than
colors. In fact, for any and such that does not divide
, there are hypergraphs having arbitrary large discrepancy and
. Apart
from constant factors (depending on and ), in these cases the symmetric
product behaves no better than the general direct product ,
which satisfies .Comment: 12 pages, no figure