About me
I have been a PhD student under the supervision of Michael Schlosser in the combinatorics group in the Institute of Mathematics at the University of Vienna. I am an alumni of the Vienna School of Mathematics and my academic work has been supported by the FWF program P 32305 ''Elliptic hypergeometric combinatorics''. I have been teaching exercise classes at the University of Natural Resources and Life Sciences (BOKU) in Vienna.
My academic work is focused on combinatorics as well as basic and elliptic hypergeometric series. The goal of my PhD thesis has been to extend special numbers, generating functions, weight functions and combinatorial identities to an elliptic level. An example of this can be found in my first paper where my coauthors and I have found a generalization of Fibonacci and Fibonomial numbers.
Since completing my PhD, I have been working as a software consultant at TNG Technology consulting.
Education
I received my PhD in Mathematics in July 2022 under the supervision of Michael Schlosser. Before that I studied Mathematics and German Philology in the teacher education programme of the University of Vienna. I wrote my Master Thesis under the supervision of Ilse Fischer in combinatorics.
Publications and preprints
Papers, Preprints and extended abstracts
Explicit formulae for generalized Stirling and Eulerian numbers
Preprint 2024: arXiv:2404.16982
Lattice paths and negatively indexed weight-dependent binomial coefficients
joint work with Michael Schlosser and Meesue Yoo, Annals of Combinatorics, 27:1–39, 2023.
- Article: Annals of Combinatorics, 27:1–39
- Preprint: arXiv:2204.05505
- Extended abstract: Séminaire Lotharingien de Combinatoire 86B (2022), Proceedings of FPSAC 2022
Elliptic and q-analogs of the Fibonomial numbers
joint work with Nantel Bergeron and Cesar Ceballos, SIGMA 16 (2020), 076, Special Issue on Elliptic Integrable Systems, Special Functions and Quantum Field Theory, 16 pages.
- Article: SIGMA 16 (2020), 076
- Preprint: arXiv:1911.12785
- Extended abstract: Séminaire Lotharingien de Combinatoire 84B (2020), Proceedings of FPSAC 2020
Thesis
Elliptic combinatorics of lattice paths, domino tilings and rook placements
Dissertation under the supervision of Michael Schlosser, 2022. PDF
Alternierende Vorzeichenmatrizen und ebene Partitionen: Eine Polytop-, Poset- und
Pyramidenperspektive (Alternating sign matrices and plane partitions: A polytope, poset and pyramidal perspective)
Master thesis under the supervision of Ilse Fischer, 2018. PDF
Schoolbooks
I have contributed additional material to the following book series:
PLUS! Mathematik für die Sekundarstufe
Authors: David Wohlhart and Michael Scharnreitner. Helbling Verlag.
Eins PLUS. Mathematik für die Volksschule
Authors: David Wohlhart, Michael Scharnreitner and Elisa Kleißner. Helbling Verlag.
Teaching
Winter term 2021/22
Exercises on Introduction to mathematical methodology (STEOP)
Winter term 2020/21
Summer term 2020
Tutorials on discrete mathematics
Winter term 2019/20
Talks and Posters
Posters
Lattice paths and negatively indexed weight-dependent binomial coefficients
Lattice Paths, Combinatorics and Interactions, hybrid conference at CIRM, June 21-25, 2021. Poster
Elliptic and q-analogs of the Fibonomial numbers
FPSAC 2020 online, Wednesday July 22th, originally planned at Bar Ilan University in Ramat Gan, Israel, July 13-17, 2020.
Additional material for the poster presentation
Talks
Lattice paths and negatively indexed weight-dependent binomial coefficients
Graduate Online Combinatorics Colloquium (GOCC), October 13, 2021. Slides
Lattice paths and negatively indexed weight-dependent binomial coefficients
AG Diskrete Mathematik, joint seminar at TU Wien and Universität Wien, June 15, 2021. Slides
Elliptic and q-analogs of the Fibonomial numbers
Seminar Series: Topics in Special Functions and Number Theory, Ashoka University (Online), January 21, 2021. Slides
Elliptic and q-analogs of the Fibonomial numbers
SFB F50 Statusseminar, Strobl, December 9, 2019. Slides
A tool to find q-analogues of special combinatorial numbers and families
Combinatorics Working Seminar, University of Vienna, November 11, 2019.
A (not yet elliptic) analog of "a q-analog of the Fibonomial numbers"
Combinatorics Working Seminar, University of Vienna, June 13, 2019.
Open Problems: Pyramidal Plane Partitions
SFB F50 Statusseminar, Strobl, December 3, 2018.
Pyramidal Plane Partitions
Combinatorics Working Seminar, University of Vienna, November 29, 2018.
Contact
josef.kuestner@univie.ac.at