  Recently Cheng et al. (Adv. in Appl. Math. 143 (2023) 102451) generalized the
inversion number to partial permutations, which are also known as Laguerre
digraphs, and asked for a suitable analogue of MacMahon's major index. We
provide such a major index, namely, the corresponding maj and inv statistics
are equidistributed, and exhibit a Haglund-Remmel-Wilson type identity. We then
interpret some Jacobi-Rogers polynomials in terms of Laguerre digraphs
generalizing Deb and Sokal's alternating Laguerre digraph interpretation of
some special Jacobi-Rogers polynomials.
