About Me

Address: 99, avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
Room: A106
Email: michaelDOTwallnerATtuwienDOTacDOTat
ORCID: 0000-0001-8581-449X

I am a PostDoc in (analytic) combinatorics working with Cyril Banderier at the Laboratoire d'Informatique de Paris Nord at the Université Paris 13. My main interests lie within (analytic) combinatorics, with an emphasis both on exact and asymptotic results for the enumeration of labelled and unlabelled structures and on probabilistic limit laws for combinatorial parameters. My main focus areas are lattice path combinatorics and tree-like structures.

Research

Publications

Peer Reviewed Conferences and Journals

  1. Divisibility of binomial coefficients by powers of two
    with Lukas Spiegelhofer; submitted to a journal.
    [ | arXiv ]
  2. The Tu-Deng conjecture holds almost surely
    with Lukas Spiegelhofer; submitted to a journal.
    [ | arXiv || Maple | Maple (PDF) ]
  3. A bijection of plane increasing trees with relaxed binary trees of right height at most one
    Submitted to a journal.
    [ | arXiv ]
  4. Asymptotic Enumeration of Compacted Binary Trees
    with Antoine Genitrini, Bernhard Gittenberger & Manuel Kauers; submitted to a journal.
    [ | arXiv ]
  5. Explicit formulas for enumeration of lattice paths: basketball and the kernel method
    with Cyril Banderier, Christian Krattenthaler, Alan Krinik, Dmitry Kruchinin, Vladimir Kruchinin & David Nguyen; accepted for publication in Developments in Mathematics Series (Springer).
    [ | arXiv ]
    • A half-normal distribution scheme for generating functions
      Full version, submitted to a journal.
      [ | arXiv ]
    • A half-normal distribution scheme for generating functions and the unexpected behavior of Motzkin paths
      To appear in Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2016), Krakow, 2016.
      [ | BibTeX | WWW | arXiv ]
    • On the shape of random Pólya structures
      with Bernhard Gittenberger & Emma Yu Jin; full version, submitted to a journal.
      [ | arXiv ]
    • A note on the scaling limits of random Polya trees
      with Bernhard Gittenberger & Emma Yu Jin; in Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Barcelona, pages 85-93, 2017.
      [ | BibTeX | WWW | arXiv ]
  6. An explicit generating function arising in counting binomial coefficients divisible by powers of primes
    with Lukas Spiegelhofer; Acta Arithmetica 181 (2017), 27-55.
    [ | WWW | arXiv ]
    • Lattice paths with catastrophes
      with Cyril Banderier; full version, Discrete Mathematics & Theoretical Computer Science, September 29, 2017, Vol 19 no. 1.
      [ | BibTeX | WWW | arXiv ]
    • Lattice paths with catastrophes
      with Cyril Banderier; Electronic Notes in Discrete Mathematics, Volume 59 (dedicated to the GAScom 2016 conference), June 2017, Pages 131–146.
      [ | BibTeX | WWW ]
    • The kernel method for lattice paths below a line of rational slope
      with Cyril Banderier; full version, accepted for publication in Developments in Mathematics Series (Springer).
      [ | arXiv ]
    • Lattice paths of slope 2/5
      with Cyril Banderier; in Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), San Diego, pages 105-113, 2015.
      [ | BibTeX | WWW | arXiv ]
    • The reflection-absorption model for directed lattice paths
      with Cyril Banderier; in Proceedings of the VIENNA young SCIENTISTS SYMPOSIUM (VSS), Vienna, pages 98-99, 2016.
      [ | BibTeX | WWW | Poster ]
    • Some reflections on lattice paths
      with Cyril Banderier; in Proceedings of the 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2014), Paris, pages 25-36, 2014.
      [ | BibTeX | WWW | arXiv ]
A list of all my publications on arxiv.org can be found here.

Theses

  1. Combinatorics of Lattice Paths and Tree-Like Structures
    PhD thesis written under the supervision of Bernhard Gittenberger, TU Wien, 2016.
    [ PDF | BibTeX ]
  2. Lattice Path Combinatorics
    Master's thesis written under the supervision of Michael Drmota, TU Wien, 2013.
    [ PDF | BibTeX ]
  3. Algebraic Multigrid Methods for Higher-Order Finite Element Discretization with parallelization
    Master's thesis written under the supervision of Matthias Maischak, Brunel University, London, 2012.
    [ PDF | BibTeX ]

Scripts

  • An Invitation to Analytic Combinatorics and Lattice Path Counting
    with Marie-Louise Lackner; lecture notes of a mini-course held at the ALEA in Europe Young Researchers' Workshop, University of Bath, Bath, UK, December 2015.
    [ PDF ]

Work in progress

  • The kernel method and Pólya urns, joint work with Hsien-Kuei Hwang (Academia Sinica).
  • Divisibility of binomial coefficients by powers of two, joint work with Lukas Spiegelhofer (TU Wien).
  • Asymptotics of general compacted trees, joint work with Antoine Genitrini (LIP6 Paris) and Bernhard Gittenberger (TU Wien).
  • Lattice paths below a line of irrational slope, joint work with Cyril Banderier (LIP13 Paris Nord).
  • Lattice path with catastrophes in higher dimensions, joint work with Cyril Banderier (LIP13 Paris Nord).
  • The half-normal law and the local time for lattice paths, joint work with Cyril Banderier (LIP13 Paris Nord).
  • Unconventional lattice path models.
  • Critical compositon schemes, joint work with Cyril Banderier (LIP13 Paris Nord) and Markus Kuba (FH-Technikum Wien).
  • The reflection-absorption model for directed lattice paths, joint work with Cyril Banderier (LIP13 Paris Nord).

Talks

  1. Lattice paths with catastrophes: limit laws and random generation, held at the Séminaire de Probabilités et Théorie Ergodique, Univeristé de Tours, France, November 2017.
  2. Limit laws for lattice paths with catastrophes, held at the séminaire de combinatoire, LIPN, Paris, France, September 2017.
  3. An introduction to lattice path counting (with catastrophes), held at the PostDoc Seminar, Institute of Statistical Science, Academia Sinica, Taiwan, July 2017.
  4. Limit laws for lattice paths with catastrophes, held at the Seminar on Combinatorics, Institute of Mathematics, Academia Sinica, Taiwan, July 2017.
  5. The kernel method for lattice paths below a line of rational slope, held at the Algo@ISS-AS Seminar, Institute of Statistical Science, Academia Sinica, Taiwan, June 2017.
  6. A note on the scaling limits of random Pólya trees, held at the Analytic Algorithmics and Combinatorics (ANALCO), Barcelona, Spain, January 2017.
  7. Compacted binary trees, held at the SFB F50 Algorithmic and Enumerative Combinatorics status seminar, Strobl, Austria, November 2016.
  8. A note on the scaling limits of random Pólya trees, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria, November 2016.
  9. Lattice paths with catastrophes, held at the 77th Séminaire Lotharingien de combinatoire (SLC77), Strobl, Austria, September 2016.
  10. A half-normal distribution scheme for generating functions, held at the Asymptotic Analysis of Algorithms & Combinatorial Structures (A3CS), Paris, France, September 2016.
  11. A half-normal distribution scheme for generating functions and the unexpected behavior of Motzkin paths, held at the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2016), Kraków, Poland, July 2016.
  12. Lattice paths below a line of rational slope, held at the Final conférence of the MADACA project, Domaine de Chalès, France, June 2016.
  13. A half-normal distribution scheme for generating functions, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria, June 2016.
  14. The reflection-absorption model for directed lattice paths, speed talk with poster presentation held at the VIENNA young SCIENTISTS SYMPOSIUM (VSS16), Vienna, Austria, June 2016.
  15. An Invitation to Analytic Combinatorics and Lattice Path Counting, mini-course with lecture notes, held at the ALEA in Europe Young Researchers' Workshop, University of Bath, Bath, UK, December 2015.
  16. Counting compacted trees, held at the SFB F50 Algorithmic and Enumerative Combinatorics status seminar, Strobl, Austria, December 2015.
  17. Why and when does the half-normal distribution appear in combinatorics?, held at the séminaire de combinatoire, LIPN, Paris, France, September 2015.
  18. A half-normal limit distribution scheme and applications to lattice paths, held at the 8th International Conference on Lattice Path Combinatorics & Applications, Cal Poly Pomona, USA, August 2015.
  19. The extension of a Rayleigh limiting distribution scheme, held at the SFB workshop on Lattice Walks, Hagenberg, Austria, May 2015.
  20. Lattice paths of slope 2/5, held at the Analytic Algorithmics and Combinatorics (ANALCO), San Diego, USA, January 2015.
  21. Lattice paths of slope 2/5, held at the SFB F50 Algorithmic and Enumerative Combinatorics status seminar, Strobl, Austria, December 2014.
  22. Lattice paths of slope 2/5 – Solving a problem of Knuth, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria, November 2014.
  23. Some (more) reflections on lattice paths, held at the probability seminar of the Université Francois Rabelais, Tours, France, September 2014.
  24. Some reflections on lattice paths, held at the 25th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2014), Paris, France, June 2014.
  25. Some reflections on directed lattice paths, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria, May 2014.
Disclaimer: All items are copyrighted either by the author or the publisher. The files available on this website are preprints. For published papers, use the corresponding publications for the final version. The copyright for published papers is owned by the publishers.

Teaching at TU Wien (in German)

Previous classes (Frühere Lehrveranstaltungen)

  • SS 2016: Diskrete Methoden, Übung
  • WS 2015: Analysis Mathematik für Informatik und Wirtschaftsinformatik, Übung
  • SS 2015: Analysis Mathematik für Informatik und Wirtschaftsinformatik, Übung
  • SS 2015: Diskrete Methoden, Übung
  • WS 2014: Analysis Mathematik für Informatik und Wirtschaftsinformatik, Übung
  • SS 2014: Algebra und Diskrete Mathematik für Informatik und Wirtschaftsinformatik, Übung
  • SS 2014: Diskrete Methoden, Übung
  • WS 2012: Numerische Mathematik, Übung

Teaching at FH Campus Wien (in German)

Previous classes (Frühere Lehrveranstaltungen)

  • WS 2016: Analysis 1, Übung für Studierende der Angewandten Elektronik
  • WS 2015: Analysis 1, Übung für Studierende der Angewandten Elektronik

Organization

Short CV

Here is a longer CV (updated 11/2017).