Research

The group's research interests are in enumerative, bijective and algebraic combinatorics. Recently, the focus has been on permutation patterns, a relatively young, but very active, research area, with several hundred papers published in the last ten years. However, the driving force behind much of our work is to find connections between families of different combinatorial structures.

Although permutations and patterns play a prominent role in our research, we have lately also been working with lattice paths, plane trees, planar maps and Ferrers diagrams with various types of fillings. The goal here is to find connections between different kinds of combinatorial objects, in the form of bijections that send a set of statistics on one side to a set of statistics on the other. Such statistics-preserving bijections not only reveal structural similarities between different combinatorial objects, they often also reveal previously unknown properties of the structures being studied.

Another interest of ours is combinatorics on words. It is a relatively new research area in Discrete Mathematics which has flourished during the last two or so decades. The motivation comes not only from different modern, as well as classical, fields of mathematics, but also from computer science, physics, and biology. In fact, many fundamental results of the theory have been discovered, or rediscovered, when using words as tools for other sciences.

We are also in the process of strenghtening our work in algebraic combinatorics, with an emphasis on algebraic and topological properties of simplicial complexes.