# About me

I am 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 a member of the Vienna School of Mathematics and supported by the FWF program P 32305 ''Elliptic hypergeometric combinatorics''. I teach exercise classes at the University of Natural Resources and Life Sciences (BOKU) in Vienna.

My current work is focused on combinatorics as well as basic and elliptic hypergeometric series. The goal of my PhD project is 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.

# Education

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. Since October 2018 I have been a PhD student at the University of Vienna under the supervision of Michael Schlosser.

# Publications and preprints

**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

**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

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.

# Talks and Posters

## Posters

**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 13th-17th, 2020.

Additional material for the poster presentation

## Talks

**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

## Office

Fakultät für Mathematik

Universität Wien

Oskar-Morgenstern-Platz 1

1090 Wien,
Österreich

Büro: 01.132