Canonical trees, compact prefix-free codes, and sums of unit fractions: a probabilistic analysis

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dc.contributor.authorHeuberger, Clemensen_ZA
dc.contributor.authorKrenn, Danielen_ZA
dc.contributor.authorWagner, Stephanen_ZA
dc.date.accessioned2016-11-30T07:57:04Z
dc.date.available2016-11-30T07:57:04Z
dc.date.issued2015
dc.descriptionCITATION: Heuberger, C., Krenn, D. & Wagner, S. 2015. Canonical trees, compact prefix-free codes, and sums of unit fractions: a probabilistic analysis. SIAM Journal on Discrete Mathematics, 29(3):1600–1653, doi:10.1137/15M1017107.
dc.descriptionThe original publication is available at http://epubs.siam.org/journal/sjdmec
dc.description.abstractFor fixed t ≥ 2, we consider the class of representations of 1 as a sum of unit fractions whose denominators are powers of t, or equivalently the class of canonical compact t-ary Huffman codes, or equivalently rooted t-ary plane “canonical” trees. We study the probabilistic behavior of the height (limit distribution is shown to be normal), the number of distinct summands (normal distribution), the path length (normal distribution), the width (main term of the expectation and concentration property), and the number of leaves at maximum distance from the root (discrete distribution).en_ZA
dc.description.urihttp://epubs.siam.org/doi/abs/10.1137/15M1017107
dc.description.versionPublisher's version
dc.format.extent54 pages
dc.identifier.citationHeuberger, C., Krenn, D. & Wagner, S. 2015. Canonical trees, compact prefix-free codes, and sums of unit fractions: a probabilistic analysis. SIAM Journal on Discrete Mathematics, 29(3):1600–1653, doi:10.1137/15M1017107.
dc.identifier.issn1095-7146 (online)
dc.identifier.issn0895-4801 (print)
dc.identifier.otherdoi:10.1137/15M1017107
dc.identifier.urihttp://hdl.handle.net/10019.1/99918
dc.language.isoen_ZAen_ZA
dc.publisherSIAM
dc.rights.holderSIAM
dc.subjectCanonical t-ary treesen_ZA
dc.subjectCompact prefix-free codesen_ZA
dc.subjectUnit fractionsen_ZA
dc.subjectLimit theorems (Probability theory)en_ZA
dc.subjectCanonical correlation (Statistics)en_ZA
dc.subjectHuffman codesen_ZA
dc.titleCanonical trees, compact prefix-free codes, and sums of unit fractions: a probabilistic analysisen_ZA
dc.typeArticleen_ZA
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