On the cd-Index for Alternating Descents - Pan, Qiongqiong; Qian, Cheng (The Electronic Journal of Combinatorics, 2024)
In 2008, Chebikin considered the cd-index of S_n with respect to the alternating descent statistic and asked for a combinatorial interpretation for its coefficients. In this paper, we provide an answer to Chebikin’s open problem in terms of permutations without double descents and ending with an ascent, with respect to a new statistic defined on these permutations. Additionally, we demonstrate a cd-index approach to proving the gamma-expansions of alternating Eulerian polynomials. Furthermore, we offer a direct combinatorial interpretation for their gamma-coefficients.