IJPAM: Volume 81, No. 6 (2012)


Ramin Kazemi
Department of Statistics
Imam Khomeini International University
Qazvin, IRAN

Abstract. In this note we discuss on a special tree structure of size $n$ which we call a $b$-increasing tree for convenience. This family of trees have the total weights $T_n=(n-1)!$. We study the quantity depth of the largest element and show that the corresponding bivariate generating function satisfies a differential equation of order $b$ where $b$ is the maximal bucket size in this model. Also we concentrate on the model, where deterministically weights are attached to the edges according to the definition of actual labels in this tree. We will use a bijection between this model and permutations. Using this bijection we obtain some results on the sum of weighted edges.

Received: July 8, 2012

AMS Subject Classification: 05C05, 60F99

Key Words and Phrases: tree structure, $b$-increasing tree, depth, weighted edge, actual labels, permutation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 6