A Riordan array is an infinite lower triangular array of numbers that is determined by a pair of generating functions meeting certain conditions. Riordan arrays can be effectively used to study many types of combinatorial problems, including the enumeration of lattice paths, plane trees and partitions. Moreover, under the right conditions Riordan arrays form a group, creating an algebraic structure out of which new combinatorial insights can be drawn. This talk will explore how the Riordan group can be used to discover interesting combinatorial identities and will also relate some well-known combinatorial problems to algebraic structure in the Riordan group. A Riordan array is an infinite lower triangular array of numbers that is determined by a pair of generating functions meeting certain conditions. Riordan arrays can be effectively used to study many types of combinatorial problems, including the enumeration of lattice paths, plane trees and partitions. Moreover, under the right conditions Riordan arrays form a group, creating an algebraic structure out of which new combinatorial insights can be drawn. This talk will explore how the Riordan group can be used to discover interesting combinatorial identities and will also relate some well-known combinatorial problems to algebraic structure in the Riordan group.
Naiomi T. Cameron is a Professor in the Department of Mathematics at Spelman College where she also currently serves as Department Chair. Her primary research interests are in enumerative and algebraic combinatorics. She shares her love of mathematics through teaching undergraduate courses, mentoring undergraduate research experiences and a variety of professional activities. She is a proud HBCU alum, having received both her Ph.D. and B.S. degrees in mathematics from Howard University. Naiomi T. Cameron is a Professor in the Department of Mathematics at Spelman College where she also currently serves as Department Chair. Her primary research interests are in enumerative and algebraic combinatorics. She shares her love of mathematics through teaching undergraduate courses, mentoring undergraduate research experiences, and a variety of professional activities. She is a proud HBCU alum, having received both her Ph.D. and B.S. degrees in mathematics from Howard University.