A Survey Of Statistics

We introduce some new Euler and Mahonian statistics defined on the symmetric group and rearrangement class of words,that have been developed in recent years,as well as some new ways to characterize them using permutation patterns.Then we describe the relationship between statistics,single distribution,double distribution and multiple distribution.The main methods introduced are bijection based on two transformations and bijections that are different from the basic transformations.In addition to the bijection also includes the idea of generating functions,it involves continuous fractions and so on.The main tool introduced is the symmetric function.Finally,the statistic that maintains the same distribution on the subset of symmetric group is slao introduced.