Abstract
A D-permutation is a permutation of [2n] satisfying 2k−1≤σ(2k−1) and 2k≥σ(2k) for all k; they provide a combinatorial model for the Genocchi and median Genocchi numbers. We find Stieltjes-type and Thron-type continued fractions for some multivariate polynomials that enumerate D-permutations with respect to a very large (sometimes infinite) number of simultaneous statistics that measure cycle status, record status, crossings and nestings.
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