Extended set partitions with successions

Abstract

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 m -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 } by successions.