[seqfan] Re: 3-dimensional arrays?

Felix Fröhlich felix.froe at gmail.com
Sat Aug 27 12:47:01 CEST 2016


thanks for your response and sorry for replying so late. I think I will go
with starting at a vertex and then reading the array layer-by-layer and
each layer row-by-row. Reading them in a spiral also sounds interesting,
but it seems to make the transition from array to sequence and vice versa a
bit more compicated (at least it seems so to me).

I think there should also be a page in the Wiki about three-dimensional
arrays. Maybe I will start one later.


2016-08-23 15:10 GMT+02:00 Chris Starling <chaosorder4 at gmail.com>:

> 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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> >
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