Type: Article
Publication Date: 2012-11-20
Citations: 17
DOI: https://doi.org/10.1109/tit.2012.2226560
The number of “nonequivalent” compact Huffman codes of length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> over an alphabet of size <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> has been studied frequently. Equivalently, the number of “nonequivalent” complete <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> -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.