From: "H. Oelschlaeger" <harald.oelschlaeger@univie.ac.at>
Newsgroups: sci.math
Subject: Re: a game
Date: Mon, 09 Nov 1998 16:32:37 -0800

This is from the Encyclopaedia Britannica:

Combinatorics and Combinatorial Geometry - Special problems.

Despite the general methods of enumeration already described, there are
many problems in which they do not apply and which therefore require
special treatment. Two of these are described below, and others will be
met further in this article.

The Ising problem.

A rectangular m x n grid is made up of unit squares, each coloured
either red or green. How many different colour patterns are there if the
number of boundary edges between red squares and green squares is
prescribed?

This problem, though easy to state, proved very difficult to solve. A
complete and rigorous solution was not achieved until the early 1960s.
The importance of the problem lies in the fact that it is the simplest
model that exhibits the macroscopic behaviour expected from certain
natural assumptions made at the microscopic level. Historically, the
problem arose from an early attempt, made in 1925, to formulate the
statistical mechanics of ferromagnetism.

The three-dimensional analogue of the Ising problem remains unsolved in
spite of persistent attacks.

So far the EB. A physicist would recognize the problem if stated like
this: each point of a quadratic lattice can assume one of two spin
states (up and down). Each pair of adjacent points with different spin
gives a certain constant contribution to the total energy. Count the
number of different configurations with a given total energy. 

At 09:32 06.11.1998 -0600, Dave Rusin wrote:
>
>Well, don't leave us in suspense! Can you summarize just what the 
>question is?
>
>dave
>
>