Journal of Mathematical Modelling and Algorithms in Operations Research

, Volume 12, Issue 4, pp 345–372

Generalized Algorithm for Restricted Weak Composition Generation

Generation Algorithm for Second-Order Restricted Weak Compositions



DOI: 10.1007/s10852-012-9194-4

Cite this article as:
Page, D.R. J Math Model Algor (2013) 12: 345. doi:10.1007/s10852-012-9194-4


This paper presents a new algorithm that arrives at a generalized solution for the generation of restricted weak compositions of n-parts. In particular, this generalized algorithm covers many commonly sought compositions such as bounded compositions, restricted compositions, weak compositions, and restricted part compositions. Introduced is an algorithm for generating generalized types of restricted weak compositions called first-order, and second-order restricted weak compositions.


Restricted compositions Restricted weak compositions Generalized algorithms Generalized compositions Generation algorithms Enumeration algorithms Integer compositions Weak integer compositions Enumeration Combinatorics Computational number theory

Mathematics Subject Classifications (2010)

68R05 68R01

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© Springer Science+Business Media B.V. 2012