Permutations, Moments, Measures

We present a continued fraction with 13 permutation statistics, several of them new, connecting great number combinatorial structures to wide variety moment sequences and their measures from classical noncommutative probability. The Hankel determinants these are product (p,q)-factorials, unifying instances the literature. corresponding capture as special cases laws, such Gaussian, Poisson, exponential, along further specializations orthogonalizing in q-Askey scheme known central limits. Statistics our generalize naturally signed colored permutations, k-arrangements introduced here, permutations k-colored fixed points.