A probabilistic approach to the descent statistic

摘要

We present a probabilistic approach to studying the descent statistic based upon a two-variable probability density, This density is log concave and. in fact, satisfies a higher order concavity condition. From these properties we derive quadratic inequalities for the descent statistic. Using Fourier series, we give exact expressions for the Euler numbers and the alternating r-signed permutations. We also obtain a probabilistic interpretation of the sin function. (C) 2002 Elsevier Science (USA). [References: 18]