Title: Bivariate P-polynomial Association Schemes on the Fibers of Uniform Posets
| Speaker: | Pierre-Antoine Bernard |
| Affiliation: | Université de Montréal |
| Location: | Please contact Sabrina Lato for the Zoom link. |
Abstract: Orthogonal polynomials emerging in the context of P- and Q-polynomial association schemes are known to reside within the Askey-scheme. This relationship forms a bridge between algebraic combinatorics and the study of special functions, yielding significant benefits for both fields. Recent research has introduced multivariate generalizations of P- and Q-polynomial association schemes and provided numerous examples. This development aims notably to deepen our understanding of multivariate analogues of Askey-Wilson polynomials. In this talk, we will review this generalization, its connection to m-distance-regular graphs, and an algebraic combinatorial structure known as a "uniform poset," from which many examples of bivariate schemes appear to originate.