[seqfan] Re: Best way to submit a bunch of snake-polycube-related sequences?

[Arthur O'Dwyer]

On Tue, Dec 27, 2022 at 8:11 AM John Mason <masonmilan33 at gmail.com> wrote:

> Hi
> Arthur's mail presents one or two terminology issues.
>
> 1. Arthur suggests that the term "strip" used in OEIS should be "snake",
> and "unholey strip" should be "strip".
> A quick google search seems to support this, so if we can say that these
> terms are consistent with the literature, then it should be OK to make the
> change.
>

FWIW, the only literature I'm *personally* aware of is Miroslav Vicher's
webpage http://www.vicher.cz/puzzle/polyform/minio/polystrip.htm . I wrote
to miroslav at vicher.cz on 2022-12-08 to see if he agreed (or disagreed) with
my interpretation of his terminology, but he didn't reply.


> Note however that "strip" is also used for other polyforms, e.g. A003104
> strip polyhexes, A151518 strip polyiamonds.
>

A003104 (strip polyhexes): I believe there is no difference between "strip
polyhex" and "snake polyhex," because hexes can never touch in any way
*other* than facewise.
A151518 (strip polyiamonds): I believe the 9-iamond with a hole *is*
included in this count, so yeah, these would be "snake" polyiamonds
according to my terminology, and the count of free "strip" polyiamonds
would start "1, 1, 1, 2, 3, 5, 8, 15, 24, 45, 78, ..." instead.(*)
A070764, A070765 (polyiamonds with/without holes): Here "hole" is again in
the sense of "region w.r.t. facewise movement." The 9-iamond with a hole
(which is a "snake non-strip" in my terminology) is included in the "with
holes" category.

(* — I just manually marked the 25 snake polyiamonds I could find in
Vicher's tiling of the 160 free 9-iamonds here
<https://www.vicher.cz/puzzle/polyform/iamond/iamonds.htm>, and saw that
that counted the holey one. Hope I didn't miss one.)


2. During the editing of A002013, the name was changed to refer to snakes
> instead of strips. But also, Ed Pegg Jr's comment was changed. So it now
> says that in 2009 Ed commented "Or, number of 2-sided snake polyominoes
> with n cells.". But he didn't. And Ed's link "Illustrations of polyforms
> <http://demonstrations.wolfram.com/PolyformExplorer/>" talks about strips,
> not snakes.
> Wouldn't it be more correct to leave Ed's comment as he originally made it,
> and add a note?
>

That's what I originally suggested! But I also thought it was a good goal
to avoid the appearance of arguing in the comments, like "This is the
sequence of Xs –Bob" "No, it's not Xs, it's Ys –Jim". (So another
possibility I suggested was to remove Ed's comment entirely.) Anyway, I'll
go along with whatever, in that department.

3. I like ouroboros. Is it already in the literature? Robert A. Russell
> used "ring" in a number of sequences, e.g. A324409. It's easier to spell
> too...
>

In the "snake-in-a-box problem," the name for a snake whose head and tail
coincide seems to be "coil" for some reason ("coil-in-a-box", see A000937).
Again I'm not aware of any literature on the subject, but to me the word
for "snake whose head meets its tail" is *self-evidently* "ouroboros"; I
can't understand why anyone would ever use any other word for it. :)  Of
course that assumes that one has already decided to call these things
"snakes."

(A324409 et alia also use "oriented" resp. "unoriented" where I've been
seeing/using "one-sided" resp. "free".)

I'd still like to hear information and/or opinions on what to do with
sequences that are linear combinations of other sequences.
Yet another example is A000577 = A070764 + A070765 (free polyiamonds = free
polyiamonds without holes + free polyiamonds with holes).
It occurs to me that for polyform-related sequences, there could be a
standard syntax for describing such sequences ("Count of
(free|one-sided|fixed|chiral) {adjective} poly{form}s {predicate}") and the
search box could be taught to combine them in standard ways (chiral =
one-sided - free; Xs without {pred} = Xs - Xs with {pred}; etc).
Or, less magic but a little more tedious, one could define derived
sequences in the comments, and the search box could be taught to scan for
comments of the form "{description} = Axxxxxx + Ayyyyyy" and so on, so that
searching terms of a derived sequence would yield the relevant comment even
if the terms didn't match any *named* sequence.
In both of these cases, it would presumably help the computerized searcher
if predictable zeroes were *not* skipped. As I understand it, OEIS has a
standard way of notating "boring elements skipped at the *beginning* of the
sequence," but not "boring elements skipped in some repeating pattern
throughout."

–Arthur