Category: math

• 2020

• Distribution of the optimal multi-pivot quicksort algorithm including explicit results for three and four pivot elements
  
  | categories: math, article, submitted | 11. January 2020 |

• 2019

• Towards a computational proof of Vizing's conjecture using semidefinite programming and sums-of-squares
  
  | categories: math, article, submitted | 16. December 2019 |
• Asymptotic analysis of regular sequences
  
  | categories: math, article, published | 25. October 2019 |
• Optimal multi-pivot quicksort and its asymptotic analysis
  
  | categories: math, talk | 17. September 2019 |
• Asymptotic analysis of regular sequences
  
  | categories: math, article, accepted | 07. September 2019 |
• On the minimal Hamming weight of a multi-base representation
  
  | categories: math, article, accepted | 20. August 2019 |
• An optimization-based sum-of-squares approach to Vizing's conjecture
  
  | categories: math, article, published | 15. July 2019 |
• Dual-pivot quicksort: Optimality, analysis and zeros of associated lattice paths
  
  | categories: math, article, published | 01. July 2019 |
• Distribution and moments of the optimal multi-pivot-quicksort
  
  | categories: math, talk | 25. June 2019 |
• Asymptotic analysis of optimal multi-pivot quicksort
  
  | categories: math, talk | 24. May 2019 |
• An optimization-based sum-of-squares approach to Vizing's conjecture
  
  | categories: math, article, accepted | 02. April 2019 |
• Algorithmic counting of nonequivalent compact Huffman codes
  
  | categories: math, article, submitted | 31. January 2019 |
• An optimization-based sum-of-squares approach to Vizing's conjecture
  
  | categories: math, article, submitted | 27. January 2019 |
• Research in the spirit of analytic combinatorics explained on the example “Quicksort algorithm”
  
  | categories: math, talk | 25. January 2019 |
• Analytic combinatorics for the mathematical analysis of algorithms
  
  | categories: math, article, thesis | 25. January 2019 |
• Esthetic numbers and lifting restrictions on the analysis of summatory functions of regular sequences
  
  | categories: math, article, published | 06. January 2019 |

• 2018

• Esthetic numbers and lifting restrictions on the analysis of summatory functions of regular sequences
  
  | categories: math, article, accepted | 01. October 2018 |
• Asymptotic analysis of regular sequences
  
  | categories: math, article, submitted | 15. September 2018 |
• On the minimal Hamming weight of a multi-base representation
  
  | categories: math, article, submitted | 20. August 2018 |
• Esthetic numbers and lifting restrictions on the analysis of summatory functions of regular sequences
  
  | categories: math, article, submitted | 02. August 2018 |
• MacMahon's Omega calculus for the analysis of optimal multi-pivot quicksort
  
  | categories: math, talk | 30. July 2018 |
• Dual-pivot quicksort: Optimality, analysis and zeros of associated lattice paths
  
  | categories: math, article, accepted | 23. July 2018 |
• Wieviele Farben werden benötigt um eine Landkarte zu färben?
  
  | categories: math, talk | 02. July 2018 |
• Analysis of summatory functions of regular sequences: Transducer and Pascal's rhombus
  
  | categories: math, talk | 28. June 2018 |
• Asymptotic expansions in SageMath
  
  | categories: math, talk | 27. June 2018 |
• Analysis of summatory functions of regular sequences: Transducer and Pascal's rhombus
  
  | categories: math, article, published | 25. June 2018 |
• Multi-base representations and their minimal Hamming weight
  
  | categories: math, talk | 24. May 2018 |
• Analysis of summatory functions of regular sequences: Transducer and Pascal's rhombus
  
  | categories: math, article, accepted | 09. April 2018 |
• Complex analysis
  
  | categories: teaching, course, math, lecture, exercises | 01. March 2018 |
• Bachelorseminar
  
  | categories: teaching, course, math, seminar | 01. March 2018 |
• Analysis of summatory functions of regular sequences: Transducer and Pascal's rhombus
  
  | categories: math, article, submitted | 09. February 2018 |
• Die Eulersche Polyederformel
  
  | categories: math, talk | 08. February 2018 |

• 2017

• Internship technical mathematics
  
  | categories: teaching, course, math, seminar | 01. October 2017 |
• Scientific texts with LaTeX and version control with Git for technical sciences
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2017 |
• Computer mathematics
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2017 |
• Algebraic structures
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2017 |
• Non-minimality of the width-w non-adjacent form in conjunction with trace one τ-adic digit expansions and Koblitz curves in characteristic two
  
  | categories: math, article, published | 15. August 2017 |
• Fluctuations in the asymptotic behavior of partial sums of k-regular sequences
  
  | categories: math, talk | 27. June 2017 |
• Precise analysis of the optimal multi-pivot quicksort
  
  | categories: math, talk | 19. June 2017 |
• k-regular sequences & mellin–perron summation for analyzing fluctuations in pascal's rhombus
  
  | categories: math, talk | 05. June 2017 |
• Analytic combinatorics
  
  | categories: math, talk | 10. May 2017 |
• Linear algebra and discrete mathematics
  
  | categories: teaching, course, math, lecture, exercises | 01. March 2017 |
• Bachelorseminar
  
  | categories: teaching, course, math, seminar | 01. March 2017 |
• The precise analysis of optimal dual-pivot quicksort and quickselect
  
  | categories: math, talk | 16. February 2017 |
• An extended note on the comparison-optimal dual-pivot quickselect
  
  | categories: math, talk | 16. January 2017 |
• An extended note on the comparison-optimal dual-pivot quickselect
  
  | categories: math, article, published | 16. January 2017 |

• 2016

• Dual-pivot quicksort: Optimality, analysis and zeros of associated lattice paths
  
  | categories: math, article, submitted | 31. October 2016 |
• Redundancy of multi-base representations of integers
  
  | categories: math, talk | 20. October 2016 |
• Non-minimality of the width-w non-adjacent form in conjunction with trace one τ-adic digit expansions and Koblitz curves in characteristic two
  
  | categories: math, article, accepted | 17. October 2016 |
• An extended note on the comparison-optimal dual-pivot quickselect
  
  | categories: math, article, accepted | 04. October 2016 |
• Computer mathematics
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2016 |
• (non-)minimal redundant digit expansions with an imaginary quadratic integer base
  
  | categories: math, talk | 06. September 2016 |
• The continuum Pólya-like random walk
  
  | categories: math, article, submitted | 03. August 2016 |
• Where are the odd entries in pascal's rhombus?
  
  | categories: math, talk | 01. August 2016 |
• An extended note on the comparison-optimal dual-pivot quickselect
  
  | categories: math, article, submitted | 18. July 2016 |
• Counting zeros in random walks on the integers and analysis of optimal dual-pivot quicksort
  
  | categories: math, article, published | 08. July 2016 |
• Counting zeros in random walks on the integers and analysis of optimal dual-pivot quicksort
  
  | categories: math, talk | 04. July 2016 |
• Asymptotic expansions in SageMath
  
  | categories: math, poster | 04. July 2016 |
• Compositions into powers of b: Asymptotic enumeration and parameters
  
  | categories: math, article, published | 10. June 2016 |
• From redundant digit expansions via continued fractions to (non-)minimal expansions
  
  | categories: math, talk | 23. May 2016 |
• Development for SageMath
  
  | categories: math, talk, sage | 22. May 2016 |
• Multiplying apples and oranges by SageMath's coercion framework
  
  | categories: math, talk, sage | 21. May 2016 |
• Automata in SageMath—combinatorics meets theoretical computer science
  
  | categories: math, article, published, sage | 10. May 2016 |
• Automata in SageMath—combinatorics meets theoretical computer science
  
  | categories: math, article, accepted, sage | 02. May 2016 |
• Counting zeros in random walks on the integers and analysis of optimal dual-pivot quicksort
  
  | categories: math, article, accepted | 22. April 2016 |
• Non-minimality of the width-w non-adjacent form in conjunction with trace one τ-adic digit expansions and Koblitz curves in characteristic two
  
  | categories: math, article, submitted | 05. April 2016 |
• Combinatorial structures
  
  | categories: teaching, course, math, lecture, exercises | 01. March 2016 |
• Counting zeros in random walks on the integers and analysis of optimal dual-pivot quicksort
  
  | categories: math, article, submitted | 12. February 2016 |
• (Fast) alles ist möglich.—Doch: Wie viele Möglichkeiten habe ich?
  
  | categories: math, talk | 04. February 2016 |
• Automata in SageMath—combinatorics meets theoretical computer science
  
  | categories: math, article, submitted, sage | 13. January 2016 |

• 2015

• A journey on a lattice path: from quicksort to hypergeometric sums and back
  
  | categories: math, talk | 25. November 2015 |
• A story about lattice paths & zeros and their relation to quicksort
  
  | categories: math, talk | 03. November 2015 |
• Asymptotic expansions in SageMath
  
  | categories: math, article, accepted, software, sage | 28. October 2015 |
• Combinatorics
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2015 |
• Computer mathematics
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2015 |
• Multi-base representations of integers: Asymptotic enumeration and central limit theorems
  
  | categories: math, article, published | 15. September 2015 |
• Canonical trees, compact prefix-free codes and sums of unit fractions: A probabilistic analysis
  
  | categories: math, article, published | 01. September 2015 |
• Compositions into powers of b: Asymptotic enumeration and parameters
  
  | categories: math, article, accepted | 27. August 2015 |
• Multi-base representations of integers: Asymptotic enumeration and central limit theorems
  
  | categories: math, article, accepted | 11. August 2015 |
• Properties of τ-adic digit expansions for fast scalar multiplication
  
  | categories: math, talk | 09. July 2015 |
• Analysis of parameters of multi-base representations of an integer
  
  | categories: math, talk | 12. June 2015 |
• Canonical trees, compact prefix-free codes and sums of unit fractions: A probabilistic analysis
  
  | categories: math, article, accepted | 08. June 2015 |
• Asymptotic properties of multi-base digit expansions of integers
  
  | categories: math, talk | 18. May 2015 |
• SageMath and GSoC 2015: (Multivariate) Asymptotic Expressions
  
  | categories: sage, math, project | 27. April 2015 |
• Various properties of redundant digit expansions: Multi-base representations of an integer
  
  | categories: math, talk | 22. April 2015 |
• Multiplying apples and oranges: Transparent arithmetic with different data types in SageMath—an introduction to SageMath's coercion framework
  
  | categories: math, talk, sage | 15. April 2015 |
• Contributing to SageMath: git and trac
  
  | categories: math, talk, sage | 14. April 2015 |
• Automata and transducers in SageMath
  
  | categories: math, talk, sage | 01. April 2015 |
• Canonical trees, compact prefix-free codes and sums of unit fractions: A probabilistic analysis
  
  | categories: math, article, submitted | 30. March 2015 |
• Multi-base representations of integers: Asymptotic enumeration and central limit theorems
  
  | categories: math, article, submitted | 29. March 2015 |
• Redundant digit expansions ... and more
  
  | categories: math, talk | 28. January 2015 |
• [link] Doctoral Program Discrete Mathematics continues
  
  | categories: link, math, project | 02. January 2015 |

• 2014

• Partitions and compositions into powers of b
  
  | categories: math, talk | 01. December 2014 |
• Some open problems concerning digit expansions and polynomial functions
  
  | categories: math, talk | 12. November 2014 |
• The number of compositions into powers of b
  
  | categories: math, article, published | 08. November 2014 |
• On the number of multi-base representations of an integer
  
  | categories: math, article, published | 08. November 2014 |
• Digit expansions with applications in cryptograpy
  
  | categories: math, poster | 03. November 2014 |
• Compositions into powers of b: Asymptotic enumeration and parameters
  
  | categories: math, article, submitted | 15. October 2014 |
• The number of multi-base representations of an integer
  
  | categories: math, talk | 18. August 2014 |
• When is non-adjacent form not a minimal digit expansion?
  
  | categories: math, talk | 10. July 2014 |
• Digit expansions with applications in cryptograpy
  
  | categories: math, poster | 10. July 2014 |
• The number of compositions into powers of b
  
  | categories: math, talk | 17. June 2014 |
• Partitions and compositions into powers of b
  
  | categories: math, talk | 19. May 2014 |
• Automata and transducers in the computer algebra system Sage
  
  | categories: math, article, submitted, sage | 29. April 2014 |
• The number of compositions into powers of b
  
  | categories: math, article, accepted | 02. April 2014 |
• On the number of multi-base representations of an integer
  
  | categories: math, article, accepted | 02. April 2014 |
• Symbolic computation
  
  | categories: teaching, course, math, lecture, exercises | 01. March 2014 |
• Mathematics II, M
  
  | categories: teaching, course, math, exercises | 01. March 2014 |
• Finite fields and coding theory
  
  | categories: teaching, course, math, exercises | 01. March 2014 |
• Bachelor thesis TM (optimization and discrete mathematics)
  
  | categories: teaching, course, math, seminar | 01. March 2014 |
• The number of compositions into powers of b
  
  | categories: math, article, submitted | 02. February 2014 |
• On the number of multi-base representations of an integer
  
  | categories: math, article, submitted | 02. February 2014 |

• 2013

• Finite state machines, automata, transducers
  
  | categories: math, article, published, software, sage | 15. December 2013 |
• Sylow p-groups of polynomial permutations on the integers mod pⁿ
  
  | categories: math, article, published | 01. December 2013 |
• Finite state machines, automata, transducers
  
  | categories: math, article, accepted, software, sage | 25. November 2013 |
• Mathematics I, M
  
  | categories: teaching, course, math, exercises | 01. October 2013 |
• Mathematical foundations of cryptography
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2013 |
• Computer mathematics
  
  | categories: teaching, course, math, exercises | 01. October 2013 |
• The width of “canonical” trees and of acyclic digraphs
  
  | categories: math, talk | 26. September 2013 |
• Optimal and non-optimal digit expansions in cryptography
  
  | categories: math, talk | 11. September 2013 |
• Finite state machines, automata, transducers
  
  | categories: math, article, submitted, software, sage | 22. August 2013 |
• Sylow p-groups of polynomial permutations on the integers mod pⁿ
  
  | categories: math, article, accepted | 29. July 2013 |
• Optimality of the width-w non-adjacent form: General characterisation and the case of imaginary quadratic bases
  
  | categories: math, article, published | 01. July 2013 |
• Existence and optimality of w-non-adjacent forms with an algebraic integer base
  
  | categories: math, article, published | 01. July 2013 |
• Analysis of the width-w non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices
  
  | categories: math, article, published | 17. June 2013 |
• The width of “canonical” trees and of acyclic digraphs
  
  | categories: math, talk | 11. June 2013 |
• Eigenschaften der Gruppe der Polynompermutationen modulo pⁿ
  
  | categories: math, talk | 15. May 2013 |
• The group of polynomial permutations modulo pⁿ
  
  | categories: math, talk | 09. April 2013 |
• The group of polynomial permutations modulo pⁿ
  
  | categories: math, talk | 22. March 2013 |
• Symbolic computation
  
  | categories: teaching, course, math, exercises | 01. March 2013 |
• Geometry processing
  
  | categories: teaching, course, math, exercises | 01. March 2013 |
• Analysis of the width-w non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices
  
  | categories: math, article, accepted | 04. February 2013 |
• Digit expansions with applications in cryptography
  
  | categories: math, talk | 25. January 2013 |
• Digit expansions with applications in cryptography
  
  | categories: math, article, thesis | 25. January 2013 |
• [link] Asymptotic Analysis of Extremal Discrete Structures
  
  | categories: link, math, project | 15. January 2013 |
• Analysis of width-w non-adjacent forms to imaginary quadratic bases
  
  | categories: math, article, published | 11. January 2013 |
• Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions
  
  | categories: math, talk | 06. January 2013 |
• Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions
  
  | categories: math, article, published | 06. January 2013 |

• 2012

• Sylow p-groups of polynomial permutations on the integers mod pⁿ
  
  | categories: math, talk | 21. December 2012 |
• Optimality of the width-w non-adjacent form: General characterisation and the case of imaginary quadratic bases
  
  | categories: math, article, accepted | 17. December 2012 |
• Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions
  
  | categories: math, talk | 01. November 2012 |
• Existence and optimality of w-non-adjacent forms with an algebraic integer base
  
  | categories: math, article, accepted | 31. October 2012 |
• Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions
  
  | categories: math, talk | 19. October 2012 |
• On linear combinations of units with bounded coefficients and double-base digit expansions
  
  | categories: math, article, published | 06. October 2012 |
• Digital expansions in conjunction with hyperelliptic curve cryptography
  
  | categories: math, poster | 02. October 2012 |
• Computer mathematics
  
  | categories: teaching, course, math, exercises | 01. October 2012 |
• Analysis of width-w non-adjacent forms to imaginary quadratic bases
  
  | categories: math, article, accepted | 25. September 2012 |
• On linear combinations of units with bounded coefficients and double-base digit expansions
  
  | categories: math, article, accepted | 24. September 2012 |
• Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions
  
  | categories: math, article, accepted | 13. September 2012 |
• Analysis of the width-w non-adjacent form in conjunction with hyperelliptic curve cryptography and with lattices
  
  | categories: math, article, submitted | 04. September 2012 |
• Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions
  
  | categories: math, article, submitted | 15. August 2012 |
• Non-adjacent forms: Optimality and analysis
  
  | categories: math, talk | 03. July 2012 |
• Analysis of the width-w non-adjacent form in conjunction with hyperelliptic curve cryptography
  
  | categories: math, talk | 07. June 2012 |
• Counting digits in non-adjacent forms in conjunction with hyperelliptic curve cryptography
  
  | categories: math, talk | 01. June 2012 |
• Analysis of non-adjacent forms in lattices
  
  | categories: math, talk | 25. May 2012 |
• On linear combinations of units with bounded coefficients and double-base digit expansions
  
  | categories: math, article, submitted | 22. May 2012 |
• Sage and GSoC 2012: Lattices
  
  | categories: sage, math, project | 30. April 2012 |
• Symbolic computation
  
  | categories: teaching, course, math, exercises | 01. March 2012 |
• Computer mathematics 2
  
  | categories: teaching, course, math, lecture, exercises | 01. March 2012 |
• Non-adjacent forms and their playground
  
  | categories: math, talk | 29. February 2012 |

• 2011

• An optimal choice of a numeral system used in elliptic curve cryptography
  
  | categories: math, talk | 16. December 2011 |
• Optimality of the width-w non-adjacent form: General characterisation and the case of imaginary quadratic bases
  
  | categories: math, article, submitted | 11. October 2011 |
• Computer mathematics 1
  
  | categories: teaching, course, math, lecture, exercises | 01. October 2011 |
• Sylow p-groups of polynomial permutations on the integers mod pⁿ
  
  | categories: math, article, submitted | 22. July 2011 |
• Analysis and optimality of the width-w non-adjacent form to imaginary quadratic bases
  
  | categories: math, talk | 01. July 2011 |
• Analysis and optimality of the width-w non-adjacent form to imaginary quadratic bases
  
  | categories: math, talk | 07. June 2011 |
• Existence and optimality of w-non-adjacent forms with an algebraic integer base
  
  | categories: math, article, submitted | 20. May 2011 |
• Non-adjacent forms and their playground
  
  | categories: math, talk | 18. March 2011 |
• Introduction to algebra
  
  | categories: teaching, course, math, exercises | 01. March 2011 |
• Discrete stochastics and information theory
  
  | categories: teaching, course, math, exercises | 01. March 2011 |
• Optimality of the width-w non-adjacent form in conjunction with Koblitz curves in characteristic three
  
  | categories: math, talk | 17. January 2011 |

• 2010

• Analysis of digital expansions to imaginary quadratic bases
  
  | categories: math, article, thesis | 11. November 2010 |
• Analysis of width-w non-adjacent forms to imaginary quadratic bases
  
  | categories: math, article, submitted | 22. August 2010 |
• Analysis of digital expansions in conjunction with Koblitz curves in characteristic three
  
  | categories: math, poster | 29. June 2010 |

• 2009

• Analytic solutions for the forward problem in electrical impedance tomography on a cylinder
  
  | categories: math, article, thesis | 28. September 2009 |

• 2008

• Polynomfunktionen und Polynompermutationen auf Z/pⁿZ
  
  | categories: math, article, thesis | 10. September 2008 |