[seqfan] Re: Quick question about self-avoiding walks
Benoît Jubin
benoit.jubin at gmail.com
Mon Dec 12 04:50:08 CET 2011
Two remarks about symmetry:
* I don't like the phrasing "reduced for symmetry" and I feel there
should be a better one. Any suggestions? Of course, we are counting
the number of orbits/equivalence classes of the given objects under
the action of some symmetry group, D_4 (dihedral) or C_4 (cyclic), see
second remark, for a square, and D_2 or C_2 for a rectangle.
* In such cases, I think it is always worth submitting the related
sequences taking into account the symmetries (rotations and
reflections; dihedral groups) AND the oriented symmetries (rotations;
cyclic groups).
Benoit
On Sun, Dec 11, 2011 at 7:21 PM, Jon Wild <wild at music.mcgill.ca> wrote:
> On Sun, 11 Dec 2011, Benoît Jubin wrote:
>
>> On Sat, Dec 10, 2011 at 6:30 AM, Jon Wild <wild at music.mcgill.ca> wrote:
>>>
>>> Look for Hamiltonian cycles on a square grid. They're only possible for
>>> squares of even side. Sequence A003763 is the main version and it
>>> references
>>> A120443, A140519 and A140521.
>>
>>
>> Jon, are these the same as meanders where you forbid the two types of
>> tiles made of two quarter-circles? If yes, this would be worth
>> mentioning, and maybe using a (probably easy) modification of your
>> program to illustrate them.
>
>
> Yes, exactly - I did this already, thinking of these restricted meanders as
> "rook's tours", and when I looked the sequence up I found they appeared
> already in the oeis as these Hamiltonian circuits. I didn't know whether it
> was worth submitting the symmetry-reduced version of the sequence. But sure,
> I'll upload some pictures to illustrate A003763, and a link between this and
> A200000.
>
> If I add tiles with a dead end, I can probably get the self-avoiding walks
> fairly easily, too--though I see Chris Gribble already has a program for
> this.
>
> Jon
>
>
>
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