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

[Wouter Meeussen]

Richard,

the example was just to clarify what I meant by 'sorted tuples'.
The concept of 'neighbourfree' means that part i cannot be followed by i+1.
With the same example that leaves only these 10:

{1, 1, 1},               {1, 1, 3}, {1, 1, 4},
                              {1, 3, 3},               {1, 4, 4},
{2, 2, 2},               {2, 2, 4},
{2, 4, 4}, {3, 3, 3},                              {4, 4, 4}

the tabular counting gives (up to 7)


    1    1    1    1    1    1    1
    2    2    2    2    2    2    2
    3    4    5    6    7    8    9
    4    7    10    13    16    19    22
    5    11    18    26    35    45    56
    6    16    30    48    70    96    126
    7    22    47    83    131    192    267

Wouter

-----Original Message----- 
From: Richard J. Mathar
Sent: Wednesday, May 06, 2020 4:58 PM
To: seqfan at list.seqfan.eu
Subject: [seqfan] Re: what are "sorted tuples" called?

wm> Date: Tue, 5 May 2020 19:04:21 +0200
wm> From: "Wouter Meeussen" <wouter.meeussen at telenet.be>
wm> To: "seqfan" <seqfan at list.seqfan.eu>
wm> Subject: [seqfan] what are "sorted tuples" called?
wm> ...
wm> I had a lot of fun trying to count the ?sorted tuples? of length n from 
an alphabet of k letters (1<=k<=n) that are neighbour-free.
wm>
wm> Example of ?sorted tuples? of length n=3 chosen from a k=4 letter 
alphabet :
wm>
wm> {1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}, {1, 2, 2},
wm> {1, 2, 3}, {1, 2, 4}, {1, 3, 3}, {1, 3, 4}, {1, 4, 4},
wm> {2, 2, 2}, {2, 2, 3}, {2, 2, 4}, {2, 3, 3}, {2, 3, 4},
wm> {2, 4, 4}, {3, 3, 3}, {3, 3, 4}, {3, 4, 4}, {4, 4, 4}
wm>
wm> I?m sure these constructs have a proper name. Any hints?

I don't understand what is  meant by "neighbour-free" (?).
As far as I can see the example counts the non-decreasing
compositions with n parts  with all parts <=k.

--
Seqfan Mailing list - http://list.seqfan.eu/