# Daniel Krenn's space

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01. November 2012

# Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions

## Abstract

For fixed \$t\ge 2\$, we consider the class of representations of \$1\$ as sum of unit fractions whose denominators are powers of \$t\$ or equivalently the class of canonical compact \$t\$-ary Huffman codes or equivalently rooted \$t\$-ary plane ``canonical'' trees.

The talk will contain results on the probabilistic behaviour of the height (limit distribution is normal), the number of distinct summands (normal distribution), the path length (normal distribution), the width (main term of the expectation and concentration property) and the number of leaves at maximum distance from the root (discrete distribution).

• This talk was given at 55th Congress of the South African Mathematical Society in Stellenbosch (South Africa), October 30–November 2, 2012.