Extended set partitions with successions

We enumerate set partitions by strings of consecutive elements, or successions, and obtain a formula for the number of partitions with successions of arbitrary length. Our approach involves direct operations on the objects within the blocks of partitions. The succession concept is extended to mm-regular partitions by means of two algorithms for transforming partitions. We also present a succession-based connection between integer partitions and set partitions, and obtain an application to the enumeration of partitions of arbitrary subsets of {1,2,…,n}{1,2,…,n} by successions.