1st Annual Alpen Adria Workshop in Combinatorics

During the semester break while students spend time on mastering the content of the semester for their exams, researchers have more time to spend on advancing research projects without any teaching. On Monday, 5 February 2024, a group of researchers in Combinatorics gathered to share progress updates and ideas relating to projects they are working on in what is hoped to be an annual event.

Taking advantage of the well-connected rail network in Austria, attendees traveled from Salzburg and Graz in the morning, and the event kicked off with lunch. Thereafter, short presentations were given on regular sequences, with Daniel Krenn (University of Salzburg) presenting a state-of-the-art overview of regular sequences, related sequences, and connections between these types of sequences. Current students within the research group of the University of Klagenfurt, Tobias Lechner and Mario Kurnig, then presented the content of their masters and bachelors projects (respectively) with progress they had each made on the study of regular sequences. Clemens Heuberger, supervisor of these projects, concluded the session with a discussion of strange phenomena that arose during these projects.

After a short coffee break, a session on bijective Combinatorics began, with Benjamin Hackl (University of Graz) presenting on the family of Fuss-Catalan objects, concluding with remarks about the height of this family of objects. Local researcher, Andrei Asinowski, discussed his FWF-funded research project on rectangulations, and his visiting student and Fulbright scholar, Michaela Polley, discussed new results involving inversion sequences (related to permutations and rectangulations). Finally, Sarah Selkirk presented work in progress around the classification of generating functions.

The day concluded with a brief open problem session, and the combination of these events led to several interesting discussions. All-in-all, the event was a success, and there have been discussions about expanding it to both an annual event and also an event for Combinatorics in Austria.

(Text by: Sarah Selkirk)