Let Y = (y1, y2, . . . ), y1 ≥ y2 ≥ · · · , be the list of sizes of the cycles in the composition of c n transpositions on the set {1, 2, . . . , n}. We prove that if c > 1/2 is constant and n → ∞, the distribution of f(c)Y/n converges to PD(1), the Poisson-Dirichlet distribution with paramenter 1, where the function f is known explicitly. A new proof is presented of the theorem by Diaconis, Ma...

We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree coalgebras is cofree and give conditions which imply that the composition is a one-sided Hopf algebra. These conditions hold when one coalgebra is a graded Hopf operad D and the other is a connected graded coalgebra w...

The idea of graph compositions, which was introduced by A. Knopfmacher and M. E. Mays, generalizes both ordinary compositions of positive integers and partitions of finite sets. In their original paper they developed formulas, generating functions, and recurrence relations for composition counting functions for several families of graphs. Here we show that some of the results involving composit...

Distributed service oriented architectures (SOAs) are increasingly used by users, who are insufficiently skilled in the art of distributed system programming. A good example are computational scientists who build large-scale distributed systems using service-oriented Grid computing infrastructures. Computational scientists use these infrastructure to build scientific applications, which are com...

The increasing complexity of software applications requires improved software development techniques in order to cope with, a.o., software reuse and evolution, the management of heterogeneous features, and the retargeting of systems towards new SW platforms. The introduction of aspect-oriented software development (AOSD) and the support for model-driven development (MDD) are two important and p...

In the classical theory of partitions, compositions were first defined by MacMahon [1] as ordered partitions. For example, there are 5 partitions and 8 compositions of 4. The partitions are 4, 31, 22, 21, 1 and the compositions are 4, 31, 13, 22, 21, 121, 12, 1. Agarwal and Andrews [2] defined an n-color partition as a partition in which a part of size n can come in n different colors. They den...

We show that the problem of computing all contiguous k-ary compositions of a sequence of n values under an associative and commutative operator requires 3 k−1 k+1n−O(k) operations. For the operator max we show in contrast that in the decision tree model the complexity is ( 1 + Θ(1/ √ k) ) n − O(k). Finally we show that the complexity of the corresponding on-line problem for the operator max is ...

Using the extended model for view-centric reasoning, EVCR, we focus on the many possibilities for concurrent processes to be composed. EVCR is an extension of VCR, both models of true concurrency; VCR is an extension of CSP, which is based on an interleaved semantics for modeling concurrency. VCR, like CSP, utilizes traces of instantaneous events, though VCR permits recording parallel events to...

A classical result by Guibas and Odlyzko obtained in 1981 gives the generating function for the number of strings that avoid a given set of substrings with the property that no substring is contained in any of the others. In this paper, we give an analogue of this result for the enumeration of compositions that avoid a given set of prohibited substrings, subject to the compositions’ length and ...