HexTheory Google Group

Re: HEX THEORY Re: Math of Hex

kogor...@gmail.com (Kevin O'Gorman) — Thu, 12 Nov 2009 14:16:53 UT

--
Kevin O'Gorman, PhD

Re: Math of Hex

kogor...@gmail.com (OHex) — Thu, 12 Nov 2009 04:30:52 UT

Some of the stuff on my theory page is somewhat mathematical. Tom Ace
even contributed his own translation of a German proof that hex is
NP-complete.

Look in [link]

++ kevin

Re: Math of Hex

kogor...@gmail.com (OHex) — Wed, 11 Nov 2009 03:09:26 UT

There are no secrets in this group -- if you could send that email,
you've got access to everything posted here. It's not much. But
there's a small repository of other things on my OHex server that may
help. Contact me directly for username/pw if you're interested, but if
you have access to a university library you'd probably do very well

RE: HEX THEORY Math of Hex

f.ma...@qut.edu.au (Frederic Maire) — Tue, 10 Nov 2009 22:58:43 UT

Hi Zach

The book by Cameron Browne contains an exhaustive bibliography (including mathematical papers).
[link]

Check also the publications of Ryan Hayward
[link]

There is the classic paper by Vadim Anshelevich available on-line
[link]

RE: HEX THEORY Math of Hex

jna...@mit.edu (Jean-Manuel Nater) — Tue, 10 Nov 2009 21:39:03 UT

this is kind of interesting.

[link]
______________________________ __________
Sent: Tuesday, November 10, 2009 4:05 PM
To: HexTheory

Hi all,

I'm a senior mathematics major at Seattle Pacific University and I'm
doing my senior project on the mathematics of Hex.

Re: HEX THEORY Math of Hex

yperc...@gmail.com (Yper Cube) — Tue, 10 Nov 2009 21:30:44 UT

Another excellent page is [link]

Re: HEX THEORY Math of Hex

yperc...@gmail.com (Yper Cube) — Tue, 10 Nov 2009 21:12:45 UT

For a start, have you checked the [link] ?
The discussions at the hex forum at littlegolem might be helpful too (with
links or views on playing tactics and strategy):
[link]
ypercube

Math of Hex

zach.br...@gmail.com (Zach) — Tue, 10 Nov 2009 21:05:45 UT

Hi all,

I'm a senior mathematics major at Seattle Pacific University and I'm
doing my senior project on the mathematics of Hex.

What I'm thinking for the project is to start my mathematical model
with a small board let's say 4x4 and then work my way to larger and
larger hex boards.

I'm a little confused as to how I can get access to the article that

Re: Edge template for half-infinite board?

kogor...@gmail.com (OHex) — Thu, 12 Feb 2009 14:40:41 UT

I think any template would be interesting to some degree, so long as
the
"allowed" region is finite. If the shapes are odd or remarkable, then
that fact becomes part of the conversation. I suppose one could judge
one template "better" than another if its "allowed" region is a subset
of
the other's, but if not then the two templates may each be useful in

Re: Edge template for half-infinite board?

na.ws...@gmail.com (na_wspak) — Thu, 12 Feb 2009 09:47:07 UT

There was similar discusion at littlegolem forum (see:
[link] )

On hexwiki there are templates up to 6th row (
[link] )

What is interesting, F14 (using standard notation) is connected to

Re: Edge template for half-infinite board?

tw...@cstone.net (twixter) — Thu, 12 Feb 2009 08:08:52 UT

Could a valid win for black involve a path which is higher than row n
at some point?
If so, there are issues of relevance to Hex theory, since most
templates involve a
presumption that the rows above could be part of other battles which
should not
be considered.

Perhaps another way of wording the problem which avoids the use of a

Re: Edge template for half-infinite board?

malcolm.r.tyrr...@gmail.com (malcolm.r.tyrrell@gmail.com) — Wed, 11 Feb 2009 16:30:26 UT

Thanks. To avoid any confusion, I've rewritten the problem so that the
bottom row is row 1.

--------8<-------------8<----- --------8<-----------

Consider an infinite half-plane of hexes, arranged so that there is a
bottom row which has no hexes underneath.

Number that row 1 and the rows above 2, 3, etc.

Re: Edge template for half-infinite board?

kogor...@gmail.com (OHex) — Wed, 11 Feb 2009 14:41:03 UT

On Feb 10, 6:13 am, "malcolm.r.tyrr...@gmail.com"

It's a really good quesion.

The tallest template I know if is on row 4 (your count; I would call
it row 5)
and needs a size-10 board to work. See [link]
for a full workup.

Looking at the templates that exist, it seems the edge length needed

Edge template for half-infinite board?

malcolm.r.tyrr...@gmail.com (malcolm.r.tyrrell@gmail.com) — Tue, 10 Feb 2009 14:13:07 UT

Hi there.

My friend and I were discussing Hex the other day when an interesting
question arose. We weren't able to resolve it at the time (although it
may be obvious). Perhaps it would interest some of you too.

--------8<-------------8<----- --------8<-----------

Consider an infinite half-plane of hexes, arranged so that there is a

Re: Hi there...

kogor...@gmail.com (OHex) — Mon, 26 Dec 2005 05:10:21 UT

As much as anything, Nash got the Nobel prize for showing that certain
finite games (a great many, actually) have an equilibrium point. This
is a state of affairs where even knowing the strategy on both sides,
neither side can gain by modifying their own strategy. In other words,
both sides have taken the optimum path. If you want to make it more