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J.D. Opdyke, Author: New General Algorithm to Enumerate Both Integer Compositions & Partitions

A Unified Approach to Algorithms Generating Unrestricted and Restricted Integer Compositions and Integer Partitions, Journal of Mathematical Modelling and Algorithms, 2010, 9(1), 53-97.


An original algorithm is presented that generates both restricted integer compositions and restricted integer partitions that can be constrained simultaneously by a) upper and lower bounds on the number of summands (“parts”) allowed, and b) upper and lower bounds on the values of those parts.  The algorithm is recursive, based directly on very fundamental mathematical constructs, and reasonably fast with good time complexity.  General solutions to the open problems of counting the number of integer compositions and integer partitions doubly restricted in this manner also are presented.  The algorithm has been used in

*  stock trading strategies and related peer reviewed publications
*  algorithms for pricing covered bonds and related peer reviewed publications
*  complexity algorithms
*  coded into other statistical languages for commercial use
*  academics’ research on combinatorial objects and their efficient enumeration


For links to examples of each of the above, and to download a preprint with SAS and Mathematica code, go to:


http://www.datamineit.com/DMI_publications.htm

or
http://ssrn.com/abstract=1231502

Tags: combinatorics, composition, fibonacci, partition, pascal

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