KIAS Workshop on Combinatorics
The Riordan group and related topics in Combinatorics and Matrix Theory
SPEAKER | Gi-Sang Cheon
INSTITUTE | Sungkyunkwan University
DATE | May 30(Thu), 2013
TIME | 14:10
PLACE | Conference room 1503, KIAS
ABSTRACT | The Riordan group is the set of in?nite lower triangular matrices whose kth column has the generating function g(z)f(z)k where g and f are elements of the ring of formal power series C[[z]] such that g(0)=1, f(0)=0 and f'(0)<>0. Such a matrix is called Riordan matrix and denoted as (g(z); f(z)) or (g; f). The Riordan group shows up naturally in a variety of combinatorial settings and combinatorial matrix theory. This talk is given by two parts. The concept of Riordan group and Riordan matrix will be introduced in the ?rst part by presenting fundamental properties and interesting subgroups. In the second part, we discuss how this concept can be applied to several problems arising in combinatorics and matrix theory.