Research Experience for Undergraduates (REU) Seminar

Title: Combinatorics and Special Functions: the Hermite Polynomials

Speaker: Dominique Foata, Institut Lothaire, Strasbourg

Date: June 16, 2005 12:30 - 2:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ


The classical orthogonal polynomials (Hermite, Laguerre, Jacobi, Meixner,...) form a hard kernel within the study of Special Functions. Several closed formulas are known, with explicit coefficients. Does there exist a hidden geometry that explains those formulas?

For a combinatorial approach we have to introduce a sequence of discrete structures, count them in two different ways, which correspond to the two sides of the identity to be proved, finally bring an algebraic tool to put the two ways together. Illustration with the Hermite polynomials.