Counting Contours on Trees

Abstract

We calculate the exact number of contours of size $n$ containing a fixed vertex in $d$-ary trees and provide sharp estimates for this number for more general trees. We also obtain a characterization of the locally finite trees with infinitely many contours of the same size containing a fixed vertex.

12 pages, 2 figures

References in corpus (1)

• A Contour Method on Cayley tree

Cited by in corpus (1)

• Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields