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

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Seiten (von - bis)	1065-1075
Fachzeitschrift	IEEE Transactions on Information Theory
Jahrgang	59
Ausgabenummer	2
DOIs	https://doi.org/10.1109/TIT.2012.2226560
Publikationsstatus	Veröffentlicht - 2013

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)
Application

Zugriff auf Dokument

10.1109/TIT.2012.2226560

Dieses zitieren

@article{f762534d27064eafbe8ff09da4dc5279,

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

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.",

author = "Christian Elsholtz and Clemens Heuberger and Helmut Prodinger",

year = "2013",

doi = "10.1109/TIT.2012.2226560",

language = "English",

volume = "59",

pages = "1065--1075",

journal = "IEEE Transactions on Information Theory",

issn = "1557-9654",

publisher = "Institute of Electrical and Electronics Engineers",

number = "2",

}

TY - JOUR

T1 - The Number of Huffman Codes, Compact Trees, and Sums of Unit Fractions

AU - Elsholtz, Christian

AU - Heuberger, Clemens

AU - Prodinger, Helmut

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

U2 - 10.1109/TIT.2012.2226560

DO - 10.1109/TIT.2012.2226560

M3 - Article

SN - 1557-9654

VL - 59

SP - 1065

EP - 1075

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 2

ER -

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

Abstract

Fields of Expertise

Treatment code (Nähere Zuordnung)

Zugriff auf Dokument

Fingerprint

Dieses zitieren