Jagged partitions and lattice paths

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A lattice-path description of K-restricted jagged partitions is presented. The corresponding lattice paths can have peaks only at even x coordinate 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: f₂ⱼ₋₁ is even and fⱼ+fⱼ₊₁≤ K-1, where fⱼ 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.