Newsgroups: sprouts-theory
From: Dan Hoey <haoyuep@aol.com>
Date: Sun, 25 Jan 2009 12:16:29 -0500
Subject: Re: A new equivalence

At 10-Dec-08, ypercube replied:
> I fear I've only scratched the surface of equivalences. I'm pretty
> sure many more can be found.  Even more, some of them, like the
> (somehow escaped from being posted last time) }0.AB.} = }2AB.} can
> have great impact on fast computing as it lowers the number of lives
> by 2 (gain-2).

I had looked at your Equivalences notes, and I'm very impressed, but
I'm afraid I haven't gotten them down well enough that I recognize
them all the time.  So please excuse me if I fail to notice that
you've sent them out first.

One thing I don't recall seeing is the case where two partial positions
differ by *[1].  The new misere Glop uses the fact that *[1]+*[1]=*[0]
to gain two ply, so these may be useful in situations where there is
another odd component:

  }1A.} = *[1] + }2A.}

}AB.}BC.}1C.} = *[1] + }ABC.}BC.}
The first is pretty obvious, but I don't know if the second has been
noticed before.

Dan