[seqfan] Re: 3-dimensional arrays?

[Chris Starling]

Hi Felix,

I asked about this a while back, and the answer seems to be that there is
no single convention for how to list the array.
What I have are several trivariate formulas that give figurate number
quantities.  Of further interest is that some arrays can be non-repeating
selections and morphs of arrays that had two or six repeated segments.  For
those, there is a difference between some or all of the variables based on
their being greater and lesser than each other.  But for the non-repeaters,
the difference in the variables came only from the formula, not the
properties of the underlying array.
I thought also about scanning arrays' triangular layers on a spiral track.
>From the center out to a vertex on one layer; then drop down to the next
layer and spiral in toward the center.  Or always start over at the
center.  Based on choices like skip or not, alternate clockwise or not, and
start as edge or center, there are at least eight ways to involve spirals.
Carry on,
-Chris

On Aug 22, 2016 10:19 AM, "Felix Fröhlich" <felix.froe at gmail.com> wrote:

> Hi
>
> is there a standard way to transform three-dimensional "cubic" arrays, say
> A(n, k, h), into sequences? If so, how exactly is this done?
>
> I understand such an array could be read by triangular "layers" or
> "cross-sections" and each such layer could then be read by rows. Is there a
> standard way to read such arrays "by triangular layer", like
> two-dimensional square arrays are read by antidiagonals? Where does one
> start and in which direction is such a layer read? And more importantly,
> how is that expressed in a sequence so one understands how to obtain the
> sequence from the array and vice-versa?
>
> Best regards
> Felix
>
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