[seqfan] Re: what are "sorted tuples" called?

Neil Sloane njasloane at gmail.com
Tue May 5 19:25:20 CEST 2020

The great Motzkin himself classified - and named - a great many objects
like the ones you are studying. Take a look at his classic paper

%H A000522 T. S. Motzkin, <a href="/A000262/a000262.pdf">Sorting numbers
for cylinders and other classification numbers</a>, in Combinatorics, Proc.
Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]

Best regards

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

On Tue, May 5, 2020 at 1:22 PM William Keith <william.keith at gmail.com>

> These are partitions into exactly three parts, with sizes at most 4.  By
> subtracting one from each part to allow zeroes, you get partitions into at
> most three parts, of size at most 3, which are counted by the q-binomial
> coefficient [6 choose 3]_q.
> Normally partitions are written in decreasing order of size.
> William
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