  In Ziegler (2002), the second author presented a lower bound for the
chromatic numbers of hypergraphs $\KG{r}{\pmb s}{\calS}$, "generalized
$r$-uniform Kneser hypergraphs with intersection multiplicities $\pmb s$." It
generalized previous lower bounds by Kriz (1992/2000) for the case ${\pmb
s}=(1,...,1)$ without intersection multiplicities, and by Sarkaria (1990) for
$\calS=\tbinom{[n]}k$. Here we discuss subtleties and difficulties that arise
for intersection multiplicities $s_i>1$:
  1. In the presence of intersection multiplicities, there are two different
versions of a "Kneser hypergraph," depending on whether one admits hypergraph
edges that are multisets rather than sets. We show that the chromatic numbers
are substantially different for the two concepts of hypergraphs. The lower
bounds of Sarkaria (1990) and Ziegler (2002) apply only to the multiset
version.
  2. The reductions to the case of prime $r$ in the proofs Sarkaria and by
Ziegler work only if the intersection multiplicities are strictly smaller than
the largest prime factor of $r$. Currently we have no valid proof for the lower
bound result in the other cases.
  We also show that all uniform hypergraphs without multiset edges can be
represented as generalized Kneser hypergraphs.
