Riordan arrays are lower triangular matrices extending infinitely to the right and downward, whose columns encode generating functions. Each Riordan array is associated with two sequences, the $A$- and $Z$- sequences. While Riordan arrays are closed under multiplication, they are not closed under addition in general. We will discuss the conditions under which the sum of two Riordan arrays yields another Riordan array, and characterize the $A$- and $Z$- sequences of this sum. This is joint work with Matias Von Bell, Eric Culver, Jessica Dickson, Stoyan Simitrov, Rachel Perrier, and Sheila Sundaram.
Sums of Riordan Arrays
Caroline Bang, Iowa State UniversityAuthors: Caroline Bang, Matias Von Bell, Eric Culver, Jessica Dickson, Stoyan Simitrov, Rachel Perrier, Sheila Sundaram.
2022 AWM Research Symposium
Women from the Graduate Research Workshop in Combinatorics