Fair Partitions - Article

After all those 'work in progress' posts on the polygon partitionig problem we posed (a series which went on for well over a year), we collected whatever we thought up into a proper article. It can be read at:

http://arxiv.org/abs/0812.2241

Note: The article is on the longer side since we try to develop the themes at a leisurely pace and try to give several illustrative examples. Hope it reads well, and even more importantly, that our arguments are logically tight. Right now, the jury is out...