Title of the course: Introduction to the Combinatorics of Permutations
Instructor: Dr. Meltem Ünel, Dr. Paul Melotti
Institution: Université Sorbonne Paris-Nord, Université Paris-Saclay
Dates: 21-27 July 2025
Prerequisites: Introductory complex analysis
Level: Graduate and advanced undergraduate
Abstract: In this course, we shall cover the basics of enumeration of permutations through different characteristics. We will start by the descents and runs of permutations, go through inversions in permutations and finally study permutations as products of cycles. In all three cases, we will employ the classical tool of generating functions to deduce exact or asymptotic enumerative results and discuss certain applications such as perfect matchings, trees and transpositions. Time permitting, we will try to conclude by a glimpse at pattern avoidance.
Language: English