Eulerian numbers and Coxeter groupsBorges Santos da Costa, João Manuel (Avtor) Konvalinka, Matjaž (Mentor) Eulerian numbersEulerian polynomialspartial orderhyperplane arrangementsCoxeter groupsEulerian numbers arise ubiquitously in various areas of mathematics. Indeed, this number sequence gives us the possibility to find several combinatorial invariants that characterize a panoply of geometric and algebraic structures. We will give a walkthrough on this beautiful counting sequence, starting with basic definitions and properties that are at the core of its combinatorial structure. Then, we introduce the notion of a partially ordered set and hyperplane arrangement, giving examples where the eulerian numbers naturally arise. Finally, there is a brief introduction to the theory of Coxeter groups, and, most importantly, how we can characterize them by using Eulerian numbers.20232023-04-13 11:39:53Magistrsko delo/naloga145213sl