Benjamin Hackl
Alpen-Adria-Universität Klagenfurt
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Publication
Featured researches published by Benjamin Hackl.
Theoretical Computer Science | 2018
Benjamin Hackl; Clemens Heuberger; Helmut Prodinger
Abstract The register function (or Horton–Strahler number) of a binary tree is a well-known combinatorial parameter. We study a reduction procedure for binary trees which offers a new interpretation for the register function as the maximal number of reductions that can be applied to a given tree. In particular, the precise asymptotic behavior of the number of certain substructures (“branches”) that occur when reducing a tree repeatedly is determined. In the same manner we introduce a reduction for simple two-dimensional lattice paths from which a complexity measure similar to the register function can be derived. We analyze this quantity, as well as the (cumulative) size of an (iteratively) reduced lattice path asymptotically.
Aequationes Mathematicae | 2018
Benjamin Hackl; Clemens Heuberger; Sara Kropf; Helmut Prodinger
Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include cutting all or only the leftmost leaves or maximal paths. This generalizes the concept of pruning a tree. The results include exact expressions and asymptotic expansions for the expected value and the variance as well as central limit theorems.
Statistics & Probability Letters | 2018
Benjamin Hackl; Helmut Prodinger
Abstract The “necklace process”, a procedure constructing necklaces of black and white beads by randomly choosing positions to insert new beads (whose color is uniquely determined based on the chosen location), is revisited. This article illustrates how, after deriving the corresponding bivariate probability generating function, the characterization of the asymptotic limiting distribution of the number of beads of a given color follows as a straightforward consequence within the analytic combinatorics framework.
Annals of Combinatorics | 2016
Benjamin Hackl; Clemens Heuberger; Helmut Prodinger; Stephan G. Wagner
Consider non-negative lattice paths ending at their maximum height, which will be called admissible paths. We show that the probability for a lattice path to be admissible is related to the Chebyshev polynomials of the first or second kind, depending on whether the lattice path is defined with a reflective barrier or not. Parameters like the number of admissible paths with given length or the expected height are analyzed asymptotically. Additionally, we use a bijection between admissible random walks and special binary sequences to prove a recent conjecture by Zhao on ballot sequences.
analytic algorithmics and combinatorics | 2017
Benjamin Hackl; Sara Kropf; Helmut Prodinger
arXiv: Combinatorics | 2016
Benjamin Hackl; Clemens Heuberger; Helmut Prodinger
arXiv: Combinatorics | 2018
Benjamin Hackl; Clemens Heuberger; Stephan G. Wagner
arXiv: Combinatorics | 2018
Benjamin Hackl; Clemens Heuberger; Helmut Prodinger
Discrete Mathematics & Theoretical Computer Science | 2018
Benjamin Hackl; Helmut Prodinger
AofA | 2018
Benjamin Hackl; Clemens Heuberger; Helmut Prodinger