Branched polymers and hyperplane arrangements

Details Branched polymers and hyperplane arrangements Branched polymers and hyperplane arrangements

2009-09-24

arxiv.org/abs/0909.4547v2

Mathematics

Combinatorics

17 pages

Scientific paper

We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie, and Kenyon and Winkler to any hyperplane arrangement A. The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A is expressed through the value of the characteristic polynomial of A at 0. We give a more general definition of the space of branched polymers, where we do not require connectivity, and introduce the notion of q-volume for it, which is expressed through the value of the characteristic polynomial of A at -q. Finally, we relate the volume of the space of branched polymers to broken circuits and show that the cohomology ring of the space of branched polymers is isomorphic to the Orlik-Solomon algebra.

Affiliated with

Also associated with

No associations

Rating

Branched polymers and hyperplane arrangements does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Branched polymers and hyperplane arrangements, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Branched polymers and hyperplane arrangements will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-325037