[seqfan] Re: A045655
Maximilian Hasler
maximilian.hasler at gmail.com
Sun Jan 1 16:04:09 CET 2012
it does not matter whether you add "reversed complement" or not,
the count will be the same whatever bijection (from { 0,...,2^n-1 }
into itself) you apply to the first and/or second component of the
pairs.
as far as I understand, the "rotations" are to be taken digit-wise in
n-bit binary words,
e.g. 011 > 110 > 101.
Maximilian
On Sun, Jan 1, 2012 at 1:18 AM, Ed Jeffery <lejeffery7 at gmail.com> wrote:
> David,
>
> It seems as if Geoffrey Critzer contradicted your definition in your title
> for A045655 by dropping your reference to "reversed complement." The
> question is, what do you mean by that terminology: are you referring to
> "ones complement" from binary arithmetic? If so, then for longer strings
> the symmetry you seem to be suggesting will be lost.
>
> If you are referring to dihedral symmetry, then, as you know, two objects
> in the plane are either (or they are not) congruent up to rotations or they
> are (or are not) reflections in a line. So, in terms of sequences of digits:
>
> Are you ordered pairs (a,b) supposed to be such that either (i) a equals b,
> or (ii) b is a reflection of a (i.e., b takes the digits of a in reverse
> order)? If so, then evidently Geoffrey Critzer's definition must be the
> correct one.
>
> It is a bit confusing, but I like your sequence.
>
> Regards,
>
> Ed Jeffery
>
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