The rank of a divisor on a finite graph: geometry and computation

Details The rank of a divisor on a finite graph: geometry and computation The rank of a divisor on a finite graph: geometry and computation

2011-11-30

arxiv.org/abs/1111.7251v1

Mathematics

Combinatorics

Scientific paper

We study the problem of computing the rank of a divisor on a finite graph, a quantity that arises in the Riemann-Roch theory on a finite graph developed by Baker and Norine (Advances of Mathematics, 215(2): 766-788, 2007). Our work consists of two parts: the first part is an algorithm whose running time is polynomial for a multigraph with a fixed number of vertices. More precisely, our algorithm has running time O(2^{n \log n})poly(size(G)), where n+1 is the number of vertices of the graph G. The second part consists of a new proof of the fact that testing if rank of a divisor is non-negative or not is in the complexity class NP intersection co-NP and motivated by this proof and its generalisations, we construct a new graph invariant that we call the critical automorphism group of the graph.

Affiliated with

Also associated with

No associations

Rating

The rank of a divisor on a finite graph: geometry and computation 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 The rank of a divisor on a finite graph: geometry and computation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The rank of a divisor on a finite graph: geometry and computation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-9242