Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage n is a non-negative integer. For any given vertex x of SG(n), we derive rigorously the probability distribution of the degree j ∈{1,2,3,4} at the vertex and its value in the infinite n limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree j. The corresponding limiting distribution φj gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as φ1=10957/40464, φ2=6626035/13636368, φ3=2943139/13636368, φ4=124895/4545456.

Source : oai:HAL:hal-00993549v1

Volume: Vol. 12 no. 3

Section: Combinatorics

Published on: January 1, 2011

Submitted on: March 26, 2015

Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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