• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,037 questions , 2,191 unanswered
5,344 answers , 22,706 comments
1,470 users with positive rep
816 active unimported users
More ...

  finding set of tree decompositions to cover all pairs of vertices

+ 3 like - 0 dislike

I first asked this on cstheory.SE but got no reply.

Let $P(X_i=x)$ represent probability that randomly chosen proper $q$-coloring of an $L\times L$ square grid contains color $x$ at position $i$. How do you efficiently compute $P(X_{i}=X_{j})$ for every pair $(i,j)$?

Fastest known method for counting $q$-proper colorings on grids uses tree decomposition. To extend it to this problem, one needs a set of tree decompositions so that every pair of vertices is contained in some bag. Is anything known about this problem?

Motivation: this is essentially two-point correlation function of Potts model, but also correlation function of self-avoiding walks and few other "all-pairs" problems face the same issue

This post imported from StackExchange MathOverflow at 2015-04-19 11:49 (UTC), posted by SE-user Yaroslav Bulatov

asked Nov 10, 2010 in Theoretical Physics by Yaroslav Bulatov (15 points) [ revision history ]
edited Apr 19, 2015 by Dilaton

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights