  In this paper1 , we use the coding developed by R. Bowen and C. Series to
compute the number of self-intersections of a closed geodesic on a pair of
pants. We give lower and upper bounds on the number of self-intersections of a
closed geodesic on a pair of pants. We prove a conjecture of Moira Chas and
Anthony Phillips in [4]. We get also bounds for the number of closed geodesics
whose self-intersection number is very close to the maximal self-intersection
number on a pair of pants
