Point of Clarification on comments below: All references to "partitions" are made equally to partitions and compositions. For example, the first and third sentences of the paper are: “A list of integers greater than zero that sum to the positive integer n is an integer partition of n. … When the ordering of the summands (“parts”) matters, these become the integer compositions of n…” The paper presents three algorithms: one for partitions, one for compositions, and one for both. Theophanes coded the one for compositions, but the comments below apply to all three.
1) THE VERY FIRST SENTENCE of the Opdyke paper reads, “A list of integers greater than zero that sum to the positive integer n is an integer partition of n.” Not sure how much more clear I can be. This is consistent throughout the paper, both via part values implied by the values of the algo’s parameters, and explicit mention in the error conditions in the code in the Appendix.
2) Re: definitions in cited papers (i.e. Kimberling): no paper can (or should) list all the conditions/caveats of all the papers it cites. That would be impossible to do, and not desireable.
3) You’re weak
partitions are so rarely used as to (arguably) not merit a mention. But just in case, the code in the paper explicitly checks if the user enters any parameter value that would require partition parts with values other than an integer greater than zero, and rejects the run with an error message. The Matlab code does not appear to do this, but it also appears to run flawlessly under the conditions explicitly listed in the paper.
4) I’m not a Matlab user but have run the Matlab code contained herein and consistent with the other comments, it has worked flawlessly on all runs tried to date.
5) A more accurate and professional comment on the code and algorithm would have been: “Users please note: as mentioned explicitly in the paper (and the code contained in the paper), the algorithm does not include weak partitions, i.e. partitions with any parts with a value of zero.” This is a clear, cogent, true statement, without gratuitous, ad hominem attacks.
6) Please spell my name correctly (‘Opdyke’ not ‘Updyke’). Everyone else who wrote it out on the page managed to; taking such care is just professional courtesy.
@Oscar, Harry, Theophanes:
Thanks for your objective (and positive) comments about your use of the code and algorithm. It is a privilege to have my paper used widely and translated into multiple languages for multiple uses (to date, in published papers on pricing covered bonds; stock trading algos; other combinatorics papers; and presentations on complexity algorithms). It has been downloaded over 7,000 times and is one of the highest rated research papers on Scrib, so I’m very pleased it appears to have been so well received. It was a lot of fun to work on and write, and I hope it is of great use to you. My sincere thanks for your interest and professionalism.