Jagged Partitions and Lattice Paths

A lattice-path description of K-restricted jagged partitions is presented. The corresponding lattice paths can have peaks only at even x coordinates and the maximal value of the height cannot be larger than K - 1. Its weight is twice that of the corresponding jagged partitions. The equivalence is demonstrated at the level of generating functions. A bijection is given between K-restricted jagged partitions and partitions restricted by the following frequencies conditions: f (2 j-1) is even and f (j) + f (j+1) a parts per thousand currency sign K - 1, where f (j) is the number of occurrences of the part j in the partition. Bijections are given between paths and these restricted partitions and between paths and partitions with successive ranks in a prescribed interval.