Avalanche polynomials

Details Avalanche polynomials Avalanche polynomials

2009-05-18

arxiv.org/abs/0905.2823v1

Mathematics

Combinatorics

16 pages

Scientific paper

The avalanche polynomial on a graph captures the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this article, we study some properties of this polynomial on plane trees. Previously it has been proved that two different trees could have the same avalanche polynomial. We show here that the problem of finding a tree with a prescribed polynomial is NP-complete. In a second part, we study the average and the variance of the avalanche distribution on trees and give a closed formula.

Affiliated with

Also associated with

No associations

Rating

Avalanche polynomials 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 Avalanche polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Avalanche polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-609315