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Experimental Mathematics Seminar

Noncommutative generalized Catalan numbers and their generating functions

Vladimir Retakh, Rutgers University

Location:  Zoom
Date & time: Thursday, 02 March 2023 at 5:00PM - 6:00PM

Abstract: In 1999 M. Aigner defined Catalan-like numbers as North-West entries of powers of semi-infinite three-diagonal matrices. In this talk I will generalize this construction to various matrices over noncommutative rings and discuss properties of the corresponding generating functions. I will also consider orthogonal polynomials associated with these "numbers". Most of the results are new even in the commutative case. Joint work with A. Berenstein and M. Gekhtman.

Zoom Link:
password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

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