The number of Huffman codes, compact trees, and sums of unit fractions
arXiv:1108.5964 · doi:10.1109/TIT.2012.2226560
Abstract
The number of "nonequivalent" Huffman codes of length r over an alphabet of size t has been studied frequently. Equivalently, the number of "nonequivalent" complete t-ary trees has been examined. We first survey the literature, unifying several independent approaches to the problem. Then, improving on earlier work we prove a very precise asymptotic result on the counting function, consisting of two main terms and an error term.