منابع مشابه
Compositions versus Cyclic Compositions
We prove that the sum of greatest common divisors of parts in all compositions of n equals the sum of lengths of all cyclic compositions of n. The proof highlights structural similarities between the set of compositions of n and the set of cyclic compositions of n. 1. Definitions and Statement A composition of the positive integer n is an ordered partition of n; that is, a vector ( ) r p p ...,...
متن کاملA Modular Model Checking Algorithm for Cyclic Feature Compositions
Feature-oriented software architecture is a way of organizing code around the features that the program provides instead of the program's objects and components. In the development of a feature-oriented software system, the developers, supplied with a set of features, select and organize features to construct the desired system. This approach, by better aligning the implementation of a system w...
متن کاملCyclic Compositions of a Positive Integer with Parts Avoiding an Arithmetic Sequence
A linear composition of a positive integer n is a finite sequence of positive integers (called parts) whose sum equals n. A cyclic composition of n is an equivalent class of all linear compositions of n that can be obtained from each other by a cyclic shift. In this paper, we enumerate the cyclic compositions of n that avoid an increasing arithmetic sequence of positive integers. In the case wh...
متن کاملCompositions and fuzzy compositions in decision-making models
In decision-making models, the compositions (Aitchison, 1986) are employed in various forms. They can represent the normalized weights of criteria in multiple-criteria decision-making models, or the probabilities of states of the world in the models of decision making under risk. The normalized weights express the relative information about the importance of criteria, while the probabilities re...
متن کاملnovel compositions and structures
We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys with large size contrast between the constituent elements, either containing small Boron atoms, or large Ca/Eu atoms, leading to quasicrystal structures quite different from currently known systems where the size contrast is smaller. Another group of ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.06.045