In my implementation of Huffman encoding, I put in a special check for equality & asked the program to print out any time an equality was found. The program never printed out anything when checking Zipf distributions from 2 to 10,000. Conjecture: When encoding a Zipf distribution using Huffman, equality never occurs. This means that we never have the case that a fraction that comes up in the Huffman encoding has two completely different decompositions into Egyptian fractions. (This Huffman encoding sorts n numbers 1/i into ascending order, then adds the two smallest, inserts that sum back into the list in order, and again adds the smallest two numbers, etc. The end result is a singleton list with the n-th harmonic number, but apparently none of the intermediate lists ever have duplicates.)