Gereralized GO

[koh]

    Dear Neil, zak, Joerg, Peter


    >1000, 47
    It is one example of parameters b(0), k.
    1000 is so large that the oscillating part is represented.

    > There iis a rule that sequences in the OEIS should not depen on a large but arbitrary parameter.

    It means many interesting sequences which depend on arbitrary parameter don't exist on OEIS.
    It is not good.

    Then I will add the Generalized GO sequence to OEUAI.
          http://boat.zero.ad.jp/~zbi74583/OEUAI-04.htm

    It is my pleasure to update OEUAI.
    Because you added almost all sequences which I submitted to OEIS so I could not update OEUAI.
 
    >GO 

    Once I submitted A096259.
    If both players don't try to win and if they put a stone on the same place when the arrangement of stones are the same then the play becomes periodic.
    Because number of the arrangements of stones are finite.
    It is 3^361.

    The sequence gives the longest period for each n points GO board.
    The origin of Generalized GO sequence is in the formula.

    >And even the length of the periods is in the EIS as
          http://www.research.att.com/~njas/sequences/A003558.

    It is interesting.
    Did you send the comment to OEIS?

    >and 2.) _slightly_ too artificial for my taste ;-)

    I agree with you.

    Try to find any property of G.GO sequence and submit the sequence related with it.




    Yasutoshi
    



IIRC, then two Beatty seqs (for a and b) have the natural numbers as
union if (and only if?) we have 1/a+1/b=1.

Here a=t=(1+sqrt(5))/2 and b=t^2:
? t=(1+sqrt(5))/2
1.61803398874989
? 1/t+1/t^2
1.00000000000000

I'd be surprised with anything as below for two
Beatty seqs not related as above.


* Kimberling, Clark <ck6 at evansville.edu> [May 17. 2008 09:01]:
> Seqfans,
>  
> Let a = (1,3,4,6,8,9,11,12,14,16,17,19,21,22,...) = A000201
> and b = (2,5,7,10,13,15,18,20,23,26,28,31,...) = A001950.
>  
> We can swap selected pairs of terms of a and b so that two nice things happen:
>  
> 1.  With each swap both a and b stay monotone (think of them as "dynamic")
> 2.  At the end, b consists solely of evens.
>  
> Right away, you can look at the above a and b, and swap pairs to get
>  
> b = (2,4,6,10,12,14,18,20,22,26,...) 
>  
> Can someone generalize?  For example, given m>1 and any k, which Beatty
> sequence-pairs allow swapping so that in the end, one of them has all terms
> congruent to k mod m?
>  
> Clark Kimberling 
>  




The 2000 Mathematics Subject Classification returns no results for "magma",
but see below results for "groupoid":

http://www.ams.org/msc/

Your search on groupoid returned the following results:

18Bxx:18B40 Groupoids, semigroupoids, semigroups, groups (viewed as
categories) [See also 20Axx, 20L05, 20Mxx]

20-xx:20L05 Groupoids (i.e. small categories in which all morphisms are
isomorphisms) {For sets with a single binary operation, see 20N02; for
topological groupoids, see 22A22, 58H05}

20Nxx:20N02 Sets with a single binary operation (groupoids)

22Axx:22A22 Topological groupoids (including differentiable and Lie
groupoids) [See also 58H05]

58-xx:58Hxx Pseudogroups, differentiable groupoids and general structures on
manifolds 

58Hxx:58H05 Pseudogroups and differentiable groupoids [See also 22A22,
22E65]

On 17/5/08 05:05, "Brendan McKay" <bdm at cs.anu.edu.au> wrote:

> I think using "groupoid" for something that is a quasigroup is just
> an error. Unless an eminent source can be found for it, I would
> recommend avoiding it completely.
> 
> Brendan.
>