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 is among the highest rated research papers on Scribd (http://www.scribd.com/explore/Research/Math-Engineering/Highest-Rated)

and has been used in

*  stock trading strategies and related peer reviewed publications (http://papers.ssrn.com/sol3/Delivery.cfm?abstractid=1494282)

*  algorithms for pricing covered bonds and related peer reviewed publications (http://www.greta.it/credit/credit2009/Poster/Kenyon.pdf)

*  complexity algorithms (http://cag.dat.demokritos.gr/Backpages/CUC.pptx)

*  coded into other statistical languages for commercial use (links: http://cag.dat.demokritos.gr/Software.php  and http://www.mathworks.com/matlabcentral/fileexchange/27110-restricte...)

*  academics’ cutting edge research on combinatorial objects and their efficient enumeration (http://www.pagewizardgames.com/enumeration_presentation_umpage7.pdf  and  http://www.pagewizardgames.com/project_umpage7.pdf)

Preprint:

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

http://www.datamineit.com/J.D.Opdyke%20-%20Fast%20Recursive%20Algor...

http://ssrn.com/abstract=1231502

SAS and Mathematica Code:

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

http://www.datamineit.com/J.D.%20Opdyke%20-%20Mathematica%20Code%20...

JMMA:

http://www.springerlink.com/content/n43n44773r0h0r11/?p=4ea1146c0de...

http://www.springerlink.com/content/l92085466093/?p=086eb6094b614ea...