Fields of interest:
Combinatorics, Statistical Physics, Special Functions, Number Theory.
The main focus of my research lies in the area of Enumerative and Algebraic Combinatorics. I am interested in all kinds of enumeration problems, on an exact or an asymptotic level. I like particularly problems that come from or are inspired by Algebra (group theory, representation theory, ...), Statistical Physics, or Number Theory. The nature of the problems that I am dealing with explains my preoccupation with hypergeometric series, which form the link in my work to Number Theory.
- A method for determining the mod-2k behaviour of recursive sequences, with applications to subgroup counting, (with M. Kauers and T. W. Müller), Electron. J. Combin. 18(2) (2012), Article P37, 83 pp.
- A dual of MacMahon's theorem on plane partitions, (with M. Ciucu), Proc. Natl. Acad. Sci. USA 110 (2013), 4518-4523.
- A Riccati differential equation and free subgroup numbers for lifts of PSL2(Z) modulo prime powers, (with T. W. Müller), J. Combin. Theory Ser. A 120 (2013), 2039-2063.