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Partitions of the set {1, 2,...,n} are classified as having successions if a block contains consecutive integers, and separated otherwise. This paper constructs enumeration formulas for such set partitions and some variations using Stirling numbers of the second kind.

A collection {S 1 ,S 2 ,...} of nonempty sets is called a complementing system of subsets for a set X of nonnegative integers if every element of X can be uniquely expressed as a sum of elements of the sets S 1 ,S 2 ,.... We present a complete characterization of all complementing systems of subsets for the set of the first n nonnegative integers as well as… (More)

The labeled factorizations of a positive integer n are obtained as a completion of the set of ordered factorizations of n. This follows a new technique for generating ordered factorizations found by extending a method for unordered factorizations that relies on partitioning the multiset of prime factors of n. Our results include explicit enumeration… (More)

We consider the enumeration of partitions of a finite set according to the number of consecutive elements inside a block under the assumption that the elements are arranged around a circle. This statistic, commonly known as circular succession, continues to play a significant role in many combinatorial problems involving combinations of a set following its… (More)

We study permutations of the set [n] = {1, 2,. .. , n} written in cycle notation, for which each cycle forms an increasing or decreasing interval of positive integers. More generally, permutations whose cycle elements form arithmetic progressions are considered. We also investigate the class of generalised interval permutations, where each cycle can be… (More)