Seminar

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Many classical combinatorial sequences are moments of positive Borel measures on the real line. Furthermore, several universal laws in probability correspond in this manner to sequences that are equally ubiquitous in combinatorics. Starting from these two observations, we explore the boundary between probability and combinatorics. We introduce a unifying combinatorial framework that brings together (and interpolates between) structures that are significant in both fields, with particular focus on permutations and set partitions. This approach gives insight into a hard open problem in combinatorics, while providing a new perspective on several classical and noncommutative limit theorems and on moments of classical orthogonal polynomials and their q-analogues. Based on joint work with Einar Steingrímsson.

Positivity And Universality (From A Combinatorial Perspective)