Monolithic Center Nakade Eyes of Size Greater than 7?

RobertJasiek · Post by **RobertJasiek** » Fri Sep 23, 2011 10:51 am

It is generally assumed to be a truth that monolithic center nakade
eyes of size greater than 7 do not exist. Has this been proven?!

hyperpape · Post by **hyperpape** » Fri Sep 23, 2011 11:03 am

What does monolithic mean? Those formed by string connected groups, surely, but what else?

jts · Post by **jts** » Fri Sep 23, 2011 1:31 pm

Click Here To Show Diagram Code: [go]$$B Corner $$ . . . . X . X . . . . $$ . . X . X . X . X . . $$ . . X . O X O . X . . $$ . . . . O X O . . . . $$ . X X O O X O O X X . $$ . . O X X X X X O . . $$ . X X O O X O O X X . $$ . . . O O X O O . . . $$ . . X . X O X . X . . $$ . . . . X . X . . . .[/go]

It would have to be a proof for larger than 10 (unless "monolithic" means something technical)

daniel_the_smith · Post by **daniel_the_smith** » Fri Sep 23, 2011 1:51 pm

Click Here To Show Diagram Code: [go]$$B One bigger? $$ . . . . X . X . . . . $$ . . X . X . X . X . . $$ . . X . O X O . X . . $$ . . . O O X O . . . . $$ . X X O X X O O X X . $$ . . O X X X X X O . . $$ . X X O O X O O X X . $$ . . . O O X O O . . . $$ . . X . X O X . X . . $$ . . . . X . X . . . .[/go]

hyperpape · Post by **hyperpape** » Fri Sep 23, 2011 2:09 pm

I'm sure monolithic places some kind of restrictions, both because it's Robert, and because it's very common knowledge that seven spaces isn't enough if you have cutting points or ataris in place.

I'm betting it will require a somewhat ugly case analysis to prove.

RobertJasiek · Post by **RobertJasiek** » Fri Sep 23, 2011 10:53 pm

In

"A library of eyes in Go, II: Monolithic eyes"

at

http://www.brocku.ca/mathematics-scienc ... ications#3

Thomas Wolf has introduced the term monolithic for "adjacent to only one [surrounding] string".

Now Erik van der Werf has provided a sketch of a proof in

<a37bb$4e7d13b4$d4bb4c13$17898@news.chello.nl>

at

https://groups.google.com/group/rec.gam ... dab1e3e4d0

with just a minor editing typo of one empty shape.

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Monolithic Center Nakade Eyes of Size Greater than 7?

Monolithic Center Nakade Eyes of Size Greater than 7?

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