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

Elsholtz, Christian; Heuberger, Clemens; Prodinger, Helmut

doi:10.1109/tit.2012.2226560

Cited by 15 publications

(26 citation statements)

References 33 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Proposition 6.2.5, we give a new characterisation of this object, using binary Huffman sequences of [8]. Proposition 6.2.10 describes the free divided level operations on this object.…”

Section: The Free Divided Power Level Algebra On One Generatormentioning

confidence: 99%

Divided Power Algebras Over an Operad

Ikonicoff¹

2019

Glasgow Math. J.

View full text Add to dashboard Cite

The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras.We describe these polynomial operations in two different ways: one way uses invariant elements under the action of the symmetric group, the other coinvariant elements. Our results are then applied to the case of level algebras, which are (non-associative) commutative algebras satisfying the exchange law.• In the set Π(r; n) there is a unique element of Comp p (n) (more precisely, in the image of Comp p (n) by ι), namely r, and Π p (n) = r∈Comp p (n) Π(r; n).

show abstract

“…In Proposition 6.2.5, we give a new characterisation of this object, using binary Huffman sequences of [8]. Proposition 6.2.10 describes the free divided level operations on this object.…”

Section: The Free Divided Power Level Algebra On One Generatormentioning

confidence: 99%

Divided Power Algebras Over an Operad

Ikonicoff¹

2019

Glasgow Math. J.

View full text Add to dashboard Cite

show abstract

“…1 for the case b = 2. Each partition corresponds to a so-called canonical tree (see [5]), and vice versa. Note that if k ∈ P m , then the resulting partition k lies in P m+s , and we clearly have …”

Section: Now Letmentioning

confidence: 99%

Compositions into Powers of b: Asymptotic Enumeration and Parameters

Krenn

Wagner

2015

Algorithmica

View full text Add to dashboard Cite

For a fixed integer base b ≥ 2, we consider the number of compositions of 1 into a given number of powers of b and, related, the maximum number of representations a positive integer can have as an ordered sum of powers of b. We study the asymptotic growth of those numbers and give precise asymptotic formulae for them, thereby improving on earlier results of Molteni. Our approach uses generating functions, which we obtain from infinite transfer matrices. With the same techniques the distribution of the largest denominator and the number of distinct parts are investigated.

show abstract

“…again [8]. In that paper, building upon a generating function approach by Flajolet and Prodinger [10], the following result has been obtained:…”

Section: Canonical Rooted T-ary Treesmentioning

confidence: 88%

“…Further formulations, details and remarks can be found in [8]. We will simply speak of an element in the class C when the particular interpretation as an element of C Partition , C Code or C Tree is not relevant.…”

Section: Canonical Rooted T-ary Treesmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Parameters of Trees Corresponding to Huffman Codes and Sums of Unit Fractions

Heuberger

Krenn

Wagner

2013

2013 Proceedings of the Tenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

Self Cite

View full text Add to dashboard Cite

For fixed t ≥ 2, we consider the class of representations of 1 as 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 behaviour 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).

show abstract

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

Cited by 15 publications

References 33 publications

Divided Power Algebras Over an Operad

Divided Power Algebras Over an Operad

Compositions into Powers of b: Asymptotic Enumeration and Parameters

Analysis of Parameters of Trees Corresponding to Huffman Codes and Sums of Unit Fractions

Contact Info

Product

Resources

About