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

[Wouter Meeussen]

thanks Neil,

(what is it with professional mathematicians? not only can they count, but 
they seem to be able to read too!
Stuff that no normal mortal can ever make sense off.  Gosh, I know I'm 
weird, but then again ...)

LOL (tongue-in-cheeck)

Wouter

-----Original Message----- 
From: Neil Sloane
Sent: Tuesday, May 05, 2020 7:25 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: what are "sorted tuples" called?

Wouter,
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

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>
wrote:

> 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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