Combinatorics Seminar
16:00-17:00
Speaker: Nikolaos Pantelidis
Title: On the Riordan Group and Riordan quasi-involutions
Abstract:
A Riordan array is a lower triangular infinite matrix, constructed by a pair of formal power series in such a way that each of the columns is generated by them, and the entries of the matrix can be determined by a recursive formula. Objects that can be expressed by a sequence of integers are used to construct Riordan arrays, such as Fibonacci or Catalan numbers.
Riordan arrays have been researched since the early 1990s and it is a growing field. Applications of them have been found in many areas of computing such as algorithm analysis, error correcting codes, wireless communications, along with scientific areas beyond the borders of Mathematics as parts of their theory and techniques have been successfully applied in Molecular Biology for RNA secondary structure enumeration and Chemistry.
In this talk, we are going to present a brief introduction to the related theory, focusing on some of our current research on the algebraic structure of the main group of Riordan arrays. We discuss conditions for Riordan elements of order 2, generalizations of them and relations between already known Riordan subgroups. Additionally, we present a type of special Riordan elements, called quasi-involutions, a factorization theorem and links to other topics.
17:00-18:00
Speaker: Jianping Pan
Title: Crystal for stable Grothendieck polynomials
Abstract: