I stopped at 5 bits with regard to orbit structure. But what interests me most is the distributional properties of the orbits rather than their lengths. Conjecture: In each orbit, there are exactly as many 0s as 1s. E.g., in the orbit 0010, 1100, 1011, 0011 you see eight 0s and eight 1s. Proof? Jim Propp On Tuesday, September 29, 2015, Allan Wechsler <acwacw@gmail.com> wrote:
This is fairly cool. 1 bit: a single 2-cycle. 2 bits: 1+3 = 4.
3 bits: a single cycle of 8.
4 bits: 4+5+7 = 16.
How far have you gone?
On Tue, Sep 29, 2015 at 9:49 AM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
I've been playing with the compound operation on bit-strings of length m in which you (a) add 1 mod 2^m and (b) reverse the order of the bits.
Has anyone seen this before? It seems sufficiently simple that I doubt I'm the first person to have played with it.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun