Descent polynomials for k bubble-sortable permutations of type B

Motivated by the work of Chung, Claesson, Dukes, and Graham (2010) [5], we define a natural type B analog of the classic bubble sort, and use it to define a type B analog of the maximum drop statistic. We enumerate (by explicit, recursive, and generating function formulas) signed permutations with r type B descents and type B maximum drop at most k. We also find a connection between these signed permutations and certain 2-colored juggling sequences.