The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions

Christian Elsholtz; Clemens Heuberger; Helmut Prodinger

doi:10.1109/TIT.2012.2226560

The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions

Christian Elsholtz, Clemens Heuberger, Helmut Prodinger

Research output: Contribution to journal › Article › peer-review

Abstract

The number of “nonequivalent” compact 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.

Original language	English
Pages (from-to)	1065-1075
Journal	IEEE Transactions on Information Theory
Volume	59
Issue number	2
DOIs	https://doi.org/10.1109/TIT.2012.2226560
Publication status	Published - 2013

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)
Application

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10.1109/TIT.2012.2226560

Cite this

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abstract = "The number of “nonequivalent” compact 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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DO - 10.1109/TIT.2012.2226560

M3 - Article

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JO - IEEE Transactions on Information Theory

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The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions

Abstract

Fields of Expertise

Treatment code (Nähere Zuordnung)

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