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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.

When the partitions of [n] = {1, 2,. .. , n} are identified with the restricted growth functions on [n], under a known bijection, certain enumeration problems for classical word statistics are formulated for set partitions. In this paper we undertake the enu-meration of partitions of [n] with respect to the number of occurrences of rises, levels and… (More)

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)

We study a special partial fraction technique which is designed for rational functions with poles on the unit circle, known as q-fractions. Even though the theory of q-partial fractions has already been applied to the Rademacher Conjecture, no systematic computational development appeared. In this paper we present two algorithms for the computation of… (More)

We classify compositions avoiding a single permutation pattern of type (2, 1) according to Wilf-equivalence and give the generating function for each of the Wilf classes.

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 new properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In particular, we establish an infinite set of Ramanujan-type congruences for the restricted overpartitions known as`-regular overpartitions. This significantly extends the recent work of Shen which focused solely on… (More)