Thematics Of Order -- Discussion

[Antti Karttunen]

Jon Awbrey wrote:

>Let me observe, however, that you are still staying largely within
>the arena of additive representations, since base representations
>are sums of products, or sums of multiples of powers of the base.
>
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BTW, this reminds me of the simple "binary/quaternary" coding of the
Game Trees (as in the Combinatorial Game Theory) I stumbled upon
a few months ago.
Unfortunately, it doesn't give an isomorphism between the
natural numbers and the equivalence classes of the game positions
in the CGT (e.g. when you collapse various dominated and reversible
positions to the same equivalence class), although it does filter
out multiple occurrences of the exactly identical branches.
I was wondering whether one could "extend" the CGT-addition
to these game tree codes, so that an addition of two trees, of which
the other or both are "non-canonical", would also yield a "non-canonical"
tree (i.e. the corresponding code).
I will later submit some associated sequences to OEIS,
time permitting.

I include a scanned JPEG-image from the page 40 of Winning Ways
as an appendix, with the margin notes in my bad handwriting...
SeqFan-server will probably balk.

 From those ten examples it should be an easy exercise
to figure the principle of encoding.

Just another proof that there's so many ways of playing
with integers, and their various representations.

Yours,

Antti

>Jon Awbrey
>
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>inquiry e-lab: http://stderr.org/pipermail/inquiry/
>o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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