Generalized Euler and Chu-Vandermonde identities

The object of this paper is to present two surprisingly general identities involving the generating functions of the number of inversions between multisets (of not necessarily uniform multiplicities). The first identity is a generalization of the Chu-Vandermonde identity, and the second a well-known identity of Euler. Our proofs are based on a one-to-one correspondence between multisubsets and certain permissible paths in a digraph with monomial weights.