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arXiv · 1108.5964

The number of Huffman codes, compact trees, and sums of unit fractions

Christian Elsholtz·Clemens Heuberger·Helmut Prodinger
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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.

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Christian Elsholtz, Clemens Heuberger, Helmut Prodinger. 2011-08-30. The number of Huffman codes, compact trees, and sums of unit fractions. https://doi.org/10.1109/tit.2012.2226560

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