Method Of Weighted Words On Cylindric Partitions

In this thesis, we study the generating functions of cylindric partitions having profilec = (c1, c2, . . . , cr) with rank 2 and levels 2,3 and 4. As a result, we give expressionsalternative to Borodin’s formula for these generating functions. We use the methodof weighted words which was first introduced by Alladi and Gordon, later was appliedby Dousse in a new version to prove some partition identities and to get infiniteproducts. We adapt the method to our subject with a more combinatorial approach.