Martingales and descent statistics

This paper develops techniques to study the asymptotic distribution of number descents in random permutations. We relax an assumption Berry-Esseen theorem Bolthausen (1982) extend theorem's scope martingale differences time-dependent variances. present its applications other combinatorial statistics as they satisfy certain recurrence relation conditions. These include inversions, signed permutations, Stirling length longest alternating subsequences, matchings and two-sided Eulerian numbers.