IJPAM: Volume 81, No. 6 (2012)
Department of Statistics
Imam Khomeini International University
Qazvin, IRAN
Abstract. In this note we discuss on a special tree structure of size
which we call a
-increasing tree for convenience.
This family of trees have the total weights
. We study
the quantity depth of the largest element and show that the
corresponding bivariate generating function satisfies a
differential equation of order
where
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, -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