News
 The website of my FWF Project P 34142 Stretched exponentials and beyond is online: https://dmg.tuwien.ac.at/mwallner/stretchedexponentials.
 Online available: My public lecture in German with the title Das 1x1 des evolutionären Stammbaums about my work on phylogenetic trees together with Cedric Chauve and Yann Ponty.
 06/2021: I am one of the organizers of Lattice Path Combinatorics and Interactions Marches aléatoires, combinatoire et interactions on June 2125, 2021 at the CIRM in Luminy, France.
 07/2021 My paper The binary digits of n+t with Lukas Spiegelhofer was accepted in the Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
 03/2021 My paper Young tableaux with periodic walls: counting with the density method with Cyril Banderier was accepted at FPSAC21.
About Me
Phone:  +43158801  104 561 
Address:  Wiedner Hauptstr. 810, A1040 Wien 
Room:  DA05 H22, Freihaus, green tower, 5th floor 
Email:  michaelDOTwallnerATtuwienDOTacDOTat 
ORCID:  000000018581449X 
At the moment I am a PostDoc and Erwin SchrödingerFellow at the Institute of Discrete Mathematics and Geometry at the TU Wien.
My interests lie in all areas of analytic and enumerative combinatorics, and in particular in interactions with probability theory, number theory, and interdisciplinary applications in computer science and computational biology.
I have studied lattice paths in one and higher dimensions, treelike structures like directed acyclic graphs, deterministic finite automata, and phylogenetic trees, as well as Young tableaux and permutation patterns.
The methods I am specialized to include
 combinatorial methods, like generating functions, the symbolic method, and bijections;
 analytic methods, like singularity analysis, saddle point analysis, and the kernel methods;
 probabilistic methods, like the method of moments and martingales.
Research
Publications
Peer Reviewed Conferences and Journals

On the critical exponents of generalized ballot sequences in three dimensions and large tandem walks
preprint.
[ Abstract and Picture  arXiv ] 
Analytic combinatorics of composition schemes and phase transitions with mixed Poisson distributions
with Cyril Banderier and Markus Kuba; preprint.
[ Abstract and Picture  arXiv ] 
Young tableaux with periodic walls: counting with the density method
with Cyril Banderier; to appear in the Proceedings of the 33rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC21).
[ Abstract and Picture ] 
The binary digits of n+t
with Lukas Spiegelhofer; accepted in the Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
[ Abstract and Picture  arXiv ] 
More Models of Walks Avoiding a Quadrant
with Mireille BousquetMélou; in Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020).
[ Abstract and Picture  BibTeX  WWW  Online Talk ] 
Latticepathology and Symmetric Functions (Extended Abstract)
with Cyril Banderier & MarieLouise Lackner; in Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020).
[ Abstract and Picture  BibTeX  WWW ] 
Asymptotics of Minimal Deterministic Finite Automata Recognizing a Finite Binary Language
with Andrew Elvey Price & Wenjie Fang; in Proceedings of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020).
[ Abstract and Picture  BibTeX  WWW  Maple  Maple (PDF) ] 
Compacted binary trees admit a stretched exponential
with Andrew Elvey Price & Wenjie Fang; accepted in the Journal of Combinatorial Theory, Series A, Volume 177, January 2021, 105306.
[ Abstract and Picture  BibTeX  WWW  arXiv  Maple  Maple (PDF) ] 
Counting and sampling gene family evolutionary histories in the duplicationloss and duplicationlosstransfer models
with Cedric Chauve & Yann Ponty; Journal of Mathematical Biology, 80(5), 13531388(2020).
[ Abstract and Picture  BibTeX  WWW  arXiv ] 

De la probabilité de creuser un tunnel
with Élie de Panafieu & Mohamed Lamine Lamali; in Proceedings of AlgoTel 2019, Saint Laurent de la Cabrerisse, 2019.
[ Abstract and Picture  BibTeX  WWW  HAL ] 
Combinatorics of nondeterministic walks of the Dyck and Motzkin type
with Élie de Panafieu & Mohamed Lamine Lamali; in Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), San Diego, 2019.
[ Abstract and Picture  BibTeX  WWW  arXiv ]

De la probabilité de creuser un tunnel

Local time for lattice paths and the associated limit laws
with Cyril Banderier; in Proceedings of GAScom 2018 conference, Athens, 2018.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 
Rectangular Young tableaux with local decreases and the density method for uniform random generation
with Cyril Banderier & Philippe Marchal; in Proceedings of GAScom 2018 conference, Athens, 2018.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 

Periodic Pólya Urns, the Density Method, and Asymptotics of Young Tableaux
with Cyril Banderier & Philippe Marchal; full version, Annals of Probability, Volume 48, Number 4 (2020), 19211965.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 
Periodic Pólya Urns and an Application to Young Tableaux
with Cyril Banderier & Philippe Marchal; in Proceedings of the 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), Uppsala, 2018.
[ Abstract and Picture  BibTeX  WWW  arXiv ]

Periodic Pólya Urns, the Density Method, and Asymptotics of Young Tableaux

Divisibility of binomial coefficients by powers of two
with Lukas Spiegelhofer; Journal of Number Theory, Volume 192, November 2018, Pages 221239.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 
The TuDeng conjecture holds almost surely
with Lukas Spiegelhofer; The Electronic Journal Combinatorics, Volume.26 (2019), no. 1, Paper 1.28, 28 pp.
[ Abstract and Picture  BibTeX  WWW  arXiv  Maple  Maple (PDF) ] 
A bijection of plane increasing trees with relaxed binary trees of right height at most one
Theoretical Computer Science,Volume 755, 10 January 2019, Pages 112.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 
Asymptotic Enumeration of Compacted Binary Trees of Bounded Right Height
with Antoine Genitrini, Bernhard Gittenberger & Manuel Kauers; to appear in Journal of Combinatorial Theory, Series A, Volume 172, May 2020, Article 105177.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 
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; Lattice Path Combinatorics and Applications, G. E. Andrews, C. Krattenthaler and A. Krinik (eds.), Developments in Mathematics, SpringerVerlag, Cham, 2019, Pages 78118.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 

A halfnormal distribution scheme for generating functions
full version, accepted in the European Journal of Combinatorics.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 
A halfnormal distribution scheme for generating functions and the unexpected behavior of Motzkin paths
In Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2016), Krakow, 2016.
[ Abstract and Picture  BibTeX  WWW  arXiv ]

A halfnormal distribution scheme for generating functions


On the shape of random Pólya structures
with Bernhard Gittenberger & Emma Yu Jin; full version, Discrete Mathematics, Volume 341, Issue 4, April 2018, Pages 896–911.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 
A note on the scaling limits of random Pólya trees
with Bernhard Gittenberger & Emma Yu Jin; in Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Barcelona, pages 8593, 2017.
[ Abstract and Picture  BibTeX  WWW  arXiv ]

On the shape of random Pólya structures
 An explicit generating function arising in counting binomial coefficients divisible by powers of primes
with Lukas Spiegelhofer; Acta Arithmetica 181 (2017), 2755.
[ Abstract and Picture  BibTeX  WWW  arXiv ] 

Lattice paths with catastrophes
with Cyril Banderier; full version, Discrete Mathematics & Theoretical Computer Science, September 29, 2017, Vol 19 no. 1.
[ Abstract and Picture  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.
[ Abstract and Picture  BibTeX  WWW ]

Lattice paths with catastrophes

 The kernel method for lattice paths below a line of rational slope
with Cyril Banderier; full version, Lattice Path Combinatorics and Applications, G. E. Andrews, C. Krattenthaler and A. Krinik (eds.), Developments in Mathematics, SpringerVerlag, Cham, 2019, Pages 119154.
[ Abstract and Picture  BibTeX  WWW  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 105113, 2015.
[ Abstract and Picture  BibTeX  WWW  arXiv ]
 The kernel method for lattice paths below a line of rational slope

 The reflectionabsorption model for directed lattice paths
with Cyril Banderier; in Proceedings of the VIENNA young SCIENTISTS SYMPOSIUM (VSS), Vienna, pages 9899, 2016.
[ Abstract and Picture  BibTeX  WWW  Poster ]  Some reflections on directed 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 2536, 2014.
[ Abstract and Picture  BibTeX  WWW  arXiv ]
 The reflectionabsorption model for directed lattice paths
Theses
 Combinatorics of Lattice Paths and TreeLike Structures
PhD thesis written under the supervision of Bernhard Gittenberger, TU Wien, 2016.
[ PDF  BibTeX ]  Lattice Path Combinatorics
Master's thesis written under the supervision of Michael Drmota, TU Wien, 2013.
[ PDF  BibTeX ]  Algebraic Multigrid Methods for HigherOrder 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 MarieLouise Lackner; lecture notes of a minicourse held at the ALEA in Europe Young Researchers' Workshop, University of Bath, Bath, UK, December 2015.
[ PDF ]
Work in progress
 Stretched exponentials in Dycklike recurrence relations, joint work with Andrew Elvey Price (LaBRI) and Wenjie Fang (UPEM).
 Walks in the 3/4plane, joint work with Mireille BousquetMélou (LaBRI).
 Critical compositon schemes, joint work with Cyril Banderier (LIP13 Paris Nord) and Markus Kuba (FHTechnikum Wien).
 The reflectionabsorption model for directed lattice paths, joint work with Cyril Banderier (LIP13 Paris Nord).
 The kernel method and Pólya urns, joint work with HsienKuei Hwang (Academia Sinica).
Talks
 Compacted binary trees and minimal automata admit stretched exponentials, held at CanaDAM 2021, Online, Canada, May 2021. [slides]
 More Models of Walks Avoiding a Quadrant, held at CanaDAM 2021, Online, Canada, May 2021. [slides]
 Das 1x1 des evolutinären Stammbaums (German), public lecture for a general audience held online at TUForMath, TU Wien (Online), Austria, May 2021.
 Periodic Pólya urns and asymptotics of Young tableaux, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, TU Wien (Online), Austria, March 2021.
 Compacted binary trees and minimal automata admit stretched exponentials, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, TU Wien (Online), Austria, January 2021.
 Compacted binary trees admit stretched exponentials, held at the Computational Logic and Applications (CLA 2020), Online, October 2020.
 Latticepathology and Symmetric Functions, recorded for the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Online, October 2020.
 More Models of Walks Avoiding a Quadrant, recorded for the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020), Online, October 2020.
 Periodic Pólya urns and asymptotics of Young tableaux, held at the Plateau Saclay Combinatorics Seminar, Online, June 2020.
 Stretched exponentials for compacted binary trees and a class of minimal automata, held at the Séminaire d'algorithmique, together with Andrew Elvey Price, UPEM, Paris, France, January 2020.
 Compacted binary trees admit a stretched exponential, held at the Seminar Combinatoire Énumérative et Algébrique, together with Andrew Elvey Price, LaBRI, Bordeaux, France, December 2019.
 Counting and Sampling Gene Families Evolutionary Histories, held at the 5th Algorithmic and Enumerative Combinatorics Summer School 2019, Hagenberg, Austria, July 2019.
 Periodic Pólya urns and an application to Young tableaux, held at the SIAM Algebraic Combinatorics Conference, Bern, Switzerland, July 2019.
 Asymptotic Enumeration of Compacted Binary Trees with Height Restrictions, held at the 30th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2019), CIRM, Marseille, France, July 2019.
 Counting and Sampling Gene Families Evolutionary Histories, held at the Seminar Combinatoire Énumérative et Algébrique, together with Cédric Chauve, LaBRI, Bordeaux, France, April 2019.
 Periodic Pólya Urns and Asymptotics of Triangular Young tableaux, held at the Journées de combinatoire de Bordeaux, LaBRI, Bordeaux, France, February 2019.
 Periodic Pólya Urns and Asymptotics of Triangular Young tableaux, held at the Séminaires de ProbabilitésStatistiques, Université de Versailles SaintQuentinenYvelines, Versailles, France, February 2019.
 Limit laws for lattice paths with catastrophes, held at the Joint Mathematics Meetings 2019, Baltimore, USA, January 2019.
 A bijection of plane increasing trees with bounded relaxed binary trees, held at the 4th Algorithmic and Enumerative Combinatorics Summer School 2018, Hagenberg, Austria, July 2018.
 Periodic Pólya urns and an application to Young tableaux, held at the 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), Uppsala, Sweden, June 2018.
 Periodic Pólya urns and an application to Young tableaux, held at the Seminar Combinatoire Énumérative et Algébrique, LaBRI, Bordeaux, France, June 2018.
 Asymptotic Enumeration of Compacted Binary Trees with Height Restrictions, held at the Computational Logic and Applications (CLA 2018), Sorbonne University, Paris, France, May 2018.
 Periodic Pólya urns and an application to Young tableaux, held at the Journée MathStic  Combinatoire, probabilités, et physique, LIPN, Paris, France, May 2018.
 A bijection of plane increasing trees with bounded relaxed binary trees, held at the Journées ALEA, CIRM, Marseille, France, March 2018.
 Asymptotic Enumeration of Compacted Binary Trees with Height Restrictions, held at the Seminar of the Combinatoire Énumérative et Algébrique, LaBRI, Bordeaux, France, February 2018.
 Halfnormal lattice paths, held at the PhD Seminars Mathematics, Ghent University, Belgium, December 2017.
 Asymptotic Enumeration of Compacted Binary Trees with Height Restrictions, held at the Seminar "Computations and Proofs" at SpecFun, INRIA, France, December 2017.
 Lattice paths with catastrophes: limit laws and random generation, held at the Séminaire de Probabilités et Théorie Ergodique, Univeristé de Tours, France, November 2017.
 Limit laws for lattice paths with catastrophes, held at the séminaire de combinatoire, LIPN, Paris, France, September 2017.
 An introduction to lattice path counting (with catastrophes), held at the PostDoc Seminar, Institute of Statistical Science, Academia Sinica, Taiwan, July 2017.
 Limit laws for lattice paths with catastrophes, held at the Seminar on Combinatorics, Institute of Mathematics, Academia Sinica, Taiwan, July 2017.
 The kernel method for lattice paths below a line of rational slope, held at the Algo@ISSAS Seminar, Institute of Statistical Science, Academia Sinica, Taiwan, June 2017.
 A note on the scaling limits of random Pólya trees, held at the Analytic Algorithmics and Combinatorics (ANALCO), Barcelona, Spain, January 2017.
 Compacted binary trees, held at the SFB F50 Algorithmic and Enumerative Combinatorics status seminar, Strobl, Austria, November 2016.
 A note on the scaling limits of random Pólya trees, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, November 2016.
 Lattice paths with catastrophes, held at the 77th Séminaire Lotharingien de combinatoire (SLC77), Strobl, Austria, September 2016.
 A halfnormal distribution scheme for generating functions, held at the Asymptotic Analysis of Algorithms & Combinatorial Structures (A3CS), Paris, France, September 2016.
 A halfnormal 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.
 Lattice paths below a line of rational slope, held at the Final conférence of the MADACA project, Domaine de Chalès, France, June 2016.
 A halfnormal distribution scheme for generating functions, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, June 2016.
 The reflectionabsorption model for directed lattice paths, speed talk with poster presentation held at the VIENNA young SCIENTISTS SYMPOSIUM (VSS16), Vienna, Austria, June 2016.
 An Invitation to Analytic Combinatorics and Lattice Path Counting, minicourse with lecture notes, held at the ALEA in Europe Young Researchers' Workshop, University of Bath, Bath, UK, December 2015.
 Counting compacted trees, held at the SFB F50 Algorithmic and Enumerative Combinatorics status seminar, Strobl, Austria, December 2015.
 Why and when does the halfnormal distribution appear in combinatorics?, held at the séminaire de combinatoire, LIPN, Paris, France, September 2015.
 A halfnormal 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.
 The extension of a Rayleigh limiting distribution scheme, held at the SFB workshop on Lattice Walks, Hagenberg, Austria, May 2015.
 Lattice paths of slope 2/5, held at the Analytic Algorithmics and Combinatorics (ANALCO), San Diego, USA, January 2015.
 Lattice paths of slope 2/5, held at the SFB F50 Algorithmic and Enumerative Combinatorics status seminar, Strobl, Austria, December 2014.
 Lattice paths of slope 2/5 – Solving a problem of Knuth, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, November 2014.
 Some (more) reflections on lattice paths, held at the probability seminar of the Université Francois Rabelais, Tours, France, September 2014.
 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.
 Some reflections on directed lattice paths, held at the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, May 2014.
Coauthors
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 and Popularization
 Member of the organizing committee of the Lattice Path Combinatorics and Interactions Marches aléatoires, combinatoire et interactions on June 2125, 2021 at the CIRM in Luminy, France.
 Member of the organizing committee of the Computational Logic and Applications 2020 (CLA20) at the TU Wien, Vienna, Austria.
 Member of the scientific and organizing committee of the L’École de Jeunes Chercheurs en Informatique Mathématique, Bordeaux, France, 2020.
 Member of the organizing committee of the ALEA in Europe Workshop, Vienna, Austria, 2017.
 Member of the organizing committee of the European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2017), Vienna, Austria, 2017.
 Member of the organizing committee of the 4th ALEA in Europe Young Researcher's Workshop, Vienna, Austria, 2016.
 Member of the organizing committee of the 26th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2015), Strobl, Austria, 2015.
 Administrator of the website of the seminar of the Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, since 2014.
 Teaching support at the Institute of Discrete Mathematics and Geometry, TU Wien, Austria, since Nov. 2013.
 09/2019: The Austrian newspaper "die Presse" published an article about my life in Bordeaux: Analysen von Algorithmen und Ahnenbäume.
 08/2019: Scilog  the science magazine of the FWF published an article about my experiences as a SchrödingerFellow in Bordeaux: Pfade und Bäume in Bordeaux (for the English version see Paths and trees in Bordeaux).
Short CV
 02/2021present: PostDoc and PI of the FWF StandAlone Project Stretched exponentials and beyond at the Institute of Discrete Mathematics and Geometry at the TU Wien;
 02/202001/2021: PostDoc and Erwin SchrödingerFellow at the Institute of Discrete Mathematics and Geometry at the TU Wien;
 02/201801/2020: PostDoc and Erwin SchrödingerFellow at the Laboratoire Bordelais de Recherche en Informatique at the Université de Bordeaux under the supervision of Mireille BousquetMélou;
 12/2017: Promotio sub auspiciis at the TU Wien;
 09/201712/2017: PostDoc at the Laboratoire d'Informatique de Paris Nord at the Université Paris 13 under the supervision of Cyril Banderier;
 05/201707/2017: PostDoc at the Academia Sinica under the supervision of HsienKuei Hwang;
 02/201704/2017: PostDoc at the TU Wien in the SFB F5003: Combinatorics of TreeLike Structures and Enriched Trees under the supervision of Bernhard Gittenberger;
 11/201301/2017: PhDstudies at TU Wien under the supervision of Bernhard Gittenberger.
 07/2011  10/2013: Technical Mathematics in Computer Sciences, TU Wien, MSc; Master thesis Lattice path combinatorics supervised by Michael Drmota.
 09/2011  09/2012: Computational Mathematics with Modelling, Brunel University London, MSc; Master thesis Algebraic Multigrid Methods for HigherOrder Finite Element Discretization with parallelization supervised by Matthias Maischak.
 10/2008  07/2011: Technical Mathematics in Computer Sciences, TU Wien, BSc; Bachelor thesis Factorization of polynomials over finite fields supervised by Michael Drmota.
 09/2001  07/2007: EDV & Organsiation, HTBL Pinkafeld; Austrian Matura.