Publications

Below you find a list of my publications. You can also visit one of my related profiles on arXiv, Google Scholar, MathSciNet, ORCID, or zbMATH.

Appeared

  1. On linear combinations of units with bounded coefficients and double-base digit expansions, joint work with Jörg Thuswaldner and Volker Ziegler, Monatsh. Math. 171 (2013), no. 3–4, 377–394.
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  2. Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions, joint work with Clemens Heuberger and Stephan Wagner, Proceedings of the Meeting on Analytic Algorithmics & Combinatorics (ANALCO), New Orleans, Louisiana, USA, January 6, 2013, SIAM, Philadelphia PA, 2013, pp. 33–42.
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  3. Analysis of width-w non-adjacent forms to imaginary quadratic bases, joint work with Clemens Heuberger, J. Number Theory 133 (2013), no. 5, 1752–1808.
    | details | arXiv | doi | mr | status: |
  4. Analysis of the width-w non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices, Theoret. Comput. Sci. 491 (2013), 47–70.
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  5. Existence and optimality of w-non-adjacent forms with an algebraic integer base, joint work with Clemens Heuberger, Acta Math. Hungar. 140 (2013), no. 1–2, 90–104.
    | details | arXiv | doi | mr | status: |
  6. Optimality of the width-w non-adjacent form: General characterisation and the case of imaginary quadratic bases, joint work with Clemens Heuberger, J. Théor. Nombres Bordeaux 25 (2013), no. 2, 353–386.
    | details | arXiv | doi | mr | status: |
  7. Sylow p-groups of polynomial permutations on the integers mod pn, joint work with Sophie Frisch, J. Number Theory 133 (2013), no. 12, 4188–4199.
    | details | arXiv | doi | pdf | status: |
  8. On the number of multi-base representations of an integer, joint work with Dimbinaina Ralaivaosaona and Stephan Wagner, 25th International Conference on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'14), DMTCS-HAL Proceedings, vol. BA, 2014, pp. 229–240.
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  9. The number of compositions into powers of b, joint work with Stephan Wagner, 25th International Conference on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'14), DMTCS-HAL Proceedings Series, vol. BA, 2014, pp. 241–252.
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  10. Canonical trees, compact prefix-free codes and sums of unit fractions: A probabilistic analysis, joint work with Clemens Heuberger and Stephan Wagner, SIAM J. Discrete Math. 29 (2015), no. 3, 1600–1653.
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  11. Multi-base representations of integers: Asymptotic enumeration and central limit theorems, joint work with Dimbinaina Ralaivaosaona and Stephan Wagner, Appl. Anal. Discrete Math. 9 (2015), no. 2, 285–312, arXiv:1503.08594.
    | details | arXiv | doi | status: |
  12. Automata in SageMath—combinatorics meets theoretical computer science, joint work with Clemens Heuberger and Sara Kropf, Discrete Math. Theor. Comput. Sci. 18 (2016), no. 3.
    | details | arXiv | link | status: |
  13. Compositions into powers of b: Asymptotic enumeration and parameters, joint work with Stephan Wagner, Algorithmica 75 (2016), no. 4, 606–631.
    | details | arXiv | doi | status: |
  14. Counting zeros in random walks on the integers and analysis of optimal dual-pivot quicksort, joint work with Martin Aumüller, Martin Dietzfelbinger, Clemens Heuberger, and Helmut Prodinger, Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 2016.
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  15. An extended note on the comparison-optimal dual-pivot quickselect, Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO) (Philadelphia PA), SIAM, 2017, pp. 115–123.
    | details | arXiv | doi | link | status: |

Accepted for publication

  1. Non-minimality of the width-w non-adjacent form in conjunction with trace one τ-adic digit expansions and Koblitz curves in characteristic two, joint work with Volker Ziegler, Math. Comp. (2017).
    | details | arXiv | link | status: accepted |

Submitted

  1. The continuum Pólya-like random walk, joint work with Hosam M. Mahmoud and Mark D. Ward, arXiv:1608.01233 [math.PR], 2016.
    | details | arXiv | link | status: |
  2. Dual-pivot quicksort: Optimality, analysis and zeros of associated lattice paths, joint work with Martin Aumüller, Martin Dietzfelbinger, Clemens Heuberger, and Helmut Prodinger, arXiv:1611.00258 [math.CO], 2016.
    | details | arXiv | link | status: |

Software

  1. Finite state machines, automata, transducers, joint work with Clemens Heuberger and Sara Kropf, http://trac.sagemath.org/15078, 2013, module in Sage 5.13.
    | details | status: software |
  2. Asymptotic expansions in SageMath, joint work with Benjamin Hackl and Clemens Heuberger, http://trac.sagemath.org/17601, 2015, module in SageMath 6.10.
    | details | status: software |

Thesis

  1. Polynomfunktionen und Polynompermutationen auf Z/pnZ, 2008, Bachelor's thesis, Graz, University of Technology.
    | details | status: thesis |
  2. Analytic solutions for the forward problem in electrical impedance tomography on a cylinder, Master's thesis, Graz, University of Technology, 2009.
    | details | status: thesis |
  3. Analysis of digital expansions to imaginary quadratic bases, Master's thesis, Graz, University of Technology, 2010.
    | details | status: thesis |
  4. Digit expansions with applications in cryptography, Ph.D. thesis, Graz, University of Technology, 2013.
    | details | link | status: thesis |