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
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2012.2226560
