Re: Any comments?

[Robert Jasiek <jasiek@xxxxxxxxxxxxxxx>]

> Does anyone like to comment on the relations of Go as a mathematical subject
> to various relavent mathematical branches (such as topology, combinatorial,
> game theory,  etc)? And give a summary of the works has been done so far?

Game theory:
- Conway, Berlekamp, Guy, and many others
- GT has been applied
- GT has been expanded to describe go in particular, esp. yose,
thermographs
- state of the art: rather high

Graph theory:
- has been applied (a go board is a graph)

Theoretical informatics:
- has been applied, esp. in CG, in abstract CG, for rules
- new algorithms have been developed or refined
- abstract AI methods have been applied or refined

Topology:
- has been applied and slightly extended for go objects

Go rules theory:
- has become an own applied maths subject
- various new definitions, rules, classifications, propositions
- connection to chaos theory suggested
- examples: definitions: TGAP, ko string, capturable living string;
rules: Conway, fixed ko, natural situational superko, various models
for Chinese, Japanese rules, etc.; classifications: game end, ko,
ko types, cycle types; propositions: equivalence scoring, score
parities, TGAP partition, optimal play for superko multiples, winning
strategy for mane go, white cannot win 0 komi game, optimal strategy
independent of small komi, etc.

Go theory:
- this shall be the formalized analysis of (high level) go terms
- countless special cases
- some attempts of generalizations and connections to other maths
subjects

-- 
robert jasiek
http://www.snafu.de/~jasiek/rules.html