The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions
Christian Elsholtz, Clemens Heuberger, Helmut Prodinger · IEEE Transactions on Information Theory · 2012
The number of “nonequivalent” compact Huffman codes of lengthrover an alphabet of sizethas been studied frequently. Equivalently, the number of “nonequivalent” completet-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.