DocumentCode
72921
Title
The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions
Author
Elsholtz, C. ; Heuberger, C. ; Prodinger, H.
Author_Institution
Inst. fur Math. A, Graz Univ. of Technol., Graz, Austria
Volume
59
Issue
2
fYear
2013
fDate
Feb. 2013
Firstpage
1065
Lastpage
1075
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.
Keywords
Huffman codes; trees (mathematics); compact Huffman codes; compact trees; counting function; nonequivalent complete t-ary trees; unit fractions; Approximation methods; Binary trees; Educational institutions; Equations; Information theory; Mathematical model; Vegetation; Algorithm design and analysis; codes; equations; sequences; tree graphs;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2012.2226560
Filename
6357294
Link To Document