Talk:Partitions

About naming conventions for orderings of the partitions

• Citation: ""Canonical" ordering of the partitions. This is the "Mathematica" ordering of the partitions."

Oh my goodness! "Canonical" = "Mathematica" and the reference is MathWorld? Come on Daniel, this wiki is not a marketing place for Dr. Wolfram and his splendid crew. Please use the mathematical definitions and place the references to commercial products in the footnotes. By the way, why do you never cite Sage or Maxima? And here some pointers to a more scientific parlance: 'lexicographic order', 'reverse lexicographic order', 'colex order', 'lexicographic order of the reflected partition sequence', 'lexicographic order of the conjugates', ... Peter Luschny 15:09, 3 January 2011 (UTC)

I found the information about ordering of partitions within the OEIS itself, from sequence pages that other people contributed:

"Canonical" partition sequence: comes from A063008 (prime factorization encoding of A080577, not A036036)

"Abramowitz and Stegun" ordering of the partitions: comes from A036036 and A036037

"Maple" ordering of the partitions: comes form A080576

"Mathematica" ordering of the partitions: comes form A080577

"Sage" ordering of the partitions: OEIS search didn't reveal any such...

"Maxima" ordering of the partitions: OEIS search didn't reveal any such...

So, from the OEIS information I obtained, Mathematica uses the canonical ordering. I'll remove any mention of Mathematica and any product/company name from the page and use the more scientific parlance exclusively. I'll not refer to any product/company name whatsoever in anything I write from now on, even if the OEIS sequence pages I'm referring to do so. I don't care about companies (especially for profit companies) of mathematical tools, I care about mathematics. — Daniel Forgues 06:43, 4 January 2011 (UTC)

Comment from N. J. A. Sloane, Jan 04 2011: (Start) There are many ways to order the partitions and there is a long-standing tradition in the OEIS to distinguish different orderings by the book or software package that uses them. This is perfectly OK, and should not be construed as an advertisement for the book or product. (End)

• A problem I see is that these names are incomprehensible for many user and will become even more incomprehensible for even more users. A mathematician looking up a sequence and not using Maple or/and Mathematica has first to make a detour and search for the meaning of these names (and this will become worse when in the future when these companies go out of business.)
• For a student today the "Handbook of Mathematical Functions" is this book: HMF. However, in this book there is no "Abramowitz and Stegun ordering" defined.
• On the other hand using mathematical definitions makes things clear for all. And there are is another benefit: the mathematical names have a mnemonic value: lexicographic, reverse and reflected etc.

Peter Luschny 17:08, 12 January 2011 (UTC)

"Abramowitz and Stegun" ordering of the partitions (parts in increasing order)

I conclude after much consideration that it is the graded reverse reflected colexicographic ordering of the partitions. These are quite tricky to check (a bit headache inducing...) It is helpful to consider, for example, that the partitions of 6 all have 6 parts, some of which may be 0. I would appreciate to have a confirmation that it is the graded reverse reflected colexicographic ordering of the partitions . — Daniel Forgues 01:31, 17 January 2011 (UTC)