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 ...

This paper examines a dataset which is modeled well by the Poisson-Log Normal process and by this process mixed with Log Normal data, which are both turned into compositions. This generates compositional data that has zeros without any need for conditional models or assuming that there is missing or censored data that needs adjustment. It also enables us to model dependence on covariates and wi...

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed-form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to...

We study the set Ak of integer sequences = ( 1; : : : ; k), de ned by 1 1 2 2 : : : k k 0; and show that the generating function is X 2Ak q j = k Y