Author

• Elahe Zohoorian Azad

Abstract

In this work, we calculate the limit distribution of the total
cost incurred by splitting a tree selected at random from the set of all
finite free trees. This total cost is considered to be an additive functional
induced by a toll equal to the square of the size of tree. The main
tools used are the recent results connecting the asymptotics of generating
functions with the asymptotics of their Hadamard product, and the
method of moments.

Keywords

• Additive functionals on trees
• Cayley trees
• Hadamard product of generating functions
• limit law
• Method of moments
• Recurrence