[seqfan] Re: Quick question about self-avoiding walks
wild at music.mcgill.ca
Mon Dec 12 04:21:20 CET 2011
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
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