[seqfan] Re: 2-dimensional arrays

[Neil Sloane]

Should the antidiagonals be read upwards or downwards?
It depends!
Usually there is an obvious choice, which is the one
that makes the result closet to a monotonic sequence.
In other words, choose the version where the antidiags are locally
increasing.

For important arrays, if there is no clear winner, include both versions.

Same answer for the question of upper-triangular vs lower triangular

This should probably be added to the help file.

Neil

On Sat, Sep 27, 2014 at 8:53 AM, Rob Arthan <rda at lemma-one.com> wrote:

> The example of a 2-dimensional array in the help page on format:
>
>         https://oeis.org/eishelp2.html#NA
>
> is a symmetric array (NIM addition), so it doesn’t make clear how you
> number the diagonals.
>
> Having looked at some examples, I think the antidiagonals are intended to
> be listed top-to-bottom
> rather than left-to-right.  Indeed, A27 seems to make this clear: the
> lattice points are enumerated like this:
>
> 1 2 4 7 ...
> 3 5 8 ...
> 6 9 ...
> 10 ...
>
> rather than like this
>
> 1 3 6 10 ...
> 2 5 9 ...
> 4 8 ...
> 7 …
>
> Is this the intention? If so, then Maybe the help page could usefully
> refer to A27.
>
> To my shame, I have contributed three 2-d arrays
> and haven’t been consistent: I used left-to-right in two of them
> and top-to-bottom in the other one. A114327 is another example
> where the left-to-right convention is implied by the formula given in the
> name.
> See below for more examples where the left-to-right convention is used.
>
> A related issue is this: many 2-d arrays enumerate features of some
> infinite list
> of finite combinatorial structures. My inclination would usually be to
> have a row
> (rather than a column) for each structure, so the rows are finitely
> non-zero.
> E.g., if I was drawing Pascal’s triangle as a square array, I would draw it
> as a lower-triangular array. A188147 is an example that follows the
> opposite convention. There are lots of examples where the tabf format has
> been used
> because otherwise there would be lots of zeroes. In examples like A188147
> and
> one I am currently working on the growth rate of the rows (in my
> convention)
> is quite fast and it makes sense to use the tabl format. Is there a
> general rule
> on whether to make the rows or the columns finite. I tried to find examples
> of this by searching for:
>
>         keyword:tabl keyword:nice ~name:triangle ~name:triangular seq:0,0
>
> This was somewhat inconclusive: it produced A55791 and A185287 as examples
> where the author’s drawing of the array follows my convention and makes
> the rows finite.
> But that isn’t what you see when you click the table link, so it looks
> like the author was
> following the left-to-right convention for enumerating the antidiagonals.
>
> Regards,
>
> Rob.
>
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>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

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
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