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Recently, Lazar and Wachs (arXiv:1910.07651) showed that the (median)Genocchi numbers play a fundamental role in the study of the homogenized Linialarrangement and obtained two new permutation models (called D-permutations andE-permutations) for (median) Genocchi numbers. They further conjecture that thedistributions of cycle numbers over the two models are equal. In a follow-up,Eu et al. (arXiv:2103.09130) further proved the gamma-positivity of the descentpolynomials of even-odd descent permutations, which are in bijection withE-permutations by Foata's fundamental transformation. This paper merges theabove two papers by considering a general moment sequence which encompasses thenumber of cycles and number of drops of E-permutations. Using the combinatorialtheory of continued fraction, the moment connection enables us to confirmLazar-Wachs' conjecture and obtain a natural $(p,q)$-analogue of Eu et al'sdescent polynomials. Furthermore, we show that the $\gamma$-coefficients of our$(p,q)$-analogue of descent polynomials have the same factorization flavor asthe $\gamma$-coeffcients of Br\"and\'en's $(p,q)$-Eulerian polynomials.

Cycles of even-odd drop permutations and continued fractions of Genocchi numbers