Person re-identification (Re-ID) is a simple task that consists recognising different persons between several non-overlapped cameras. The Re-ID system is divided into two main stages: 1) extracting feature representations to construct a person's appearance signature; 2) establishing the correspondence/matching by learning similarity metrics or ranking functions. However, person Re-ID is a challenging task due to similarity of human's appearance. This paper provides a representation of the appearance descriptors, called signatures, for multi-shot person Re-ID. First, we will present the tracklets, i.e., trajectories of persons. Then, we compute the signature and represent it based on the approach of part appearance mixture (PAM). An evaluation of the quality of this signature representation is also described in order to essentially solve the problems of high variance in a person's appearance, occlusions, illumination changes and person's pose. Experiments and results on two public datasets and on our own dataset show good performances.