The relation between properties of Gentile statistics and fractional statistics of anyon

In this paper, we discuss the relationship of two kinds of intermediate-statistics, the Gentile statistics and the fractional statistics of anyons. The anyon winding number representation is introduced. We construct the transformation between anyon winding number representation and the occupation number representation of particles of Gentile statistics. We study intermediate-statistics quantum bracket and coherent states for anyons in the winding number representation. We demonstrate that anyons can be simulated by Gentile statistics with a geometric phase