$q$-enumeration of type B and D Eulerian polynomials based on parity of descents

Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian

Carlitz and Scoville in 1973 considered a four variable polynomial that enumerates permutations in ${\mathfrak{S}}_n$ with respect to the parity of its descents and ascents. In recen…