  Worpitzky's identity expresses $n^p$ in terms of the Eulerian numbers and
binomial coefficients: $$n^p = \sum_{i=0}^{p-1} \genfrac<>{0pt}{}{p}{i}
\binom{n+i}{p}.$$
  Pita-Ruiz recently defined numbers $A_{a,b,r}(p,i)$ implicitly to satisfy a
generalized Worpitzky identity $$\binom{an+b}{r}^p = \sum_{i=0}^{rp}
A_{a,b,r}(p,i) \binom{n+rp-i}{rp},$$ and asked whether there is a combinatorial
interpretation of the numbers $A_{a,b,r}(p,i)$.
  We provide such a combinatorial interpretation by defining a notion of
descents in colored multipermutations, and then proving that $A_{a,b,r}(p,i)$
is equal to the number of colored multipermutations of $\{1^r, 2^r, \ldots,
p^r\}$ with $a$ colors and $i$ weak descents. We use this to give combinatorial
proofs of several identities involving $A_{a,b,r}(p,i)$, including the
aforementioned generalized Worpitzky identity.
