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Washington State
University

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics and Statistics

Meet at Zoom

March 22, Monday, 4:10 - 5:00 PM

Jessica Dickson

Department of Mathematics and Statistics

Washington State University

Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar

Department of Mathematics and Statistics

Meet at Zoom

March 22, Monday, 4:10 - 5:00 PM

Jessica Dickson

Department of Mathematics and Statistics

Washington State University

Title: The A- to Z-series of Riordan Arrays

Abstract: Riordan arrays can be thought of as upper triangular arrays that extend infinitely to the right and downwards; we can consider these as matrices indexed on the non-negative integers. Extended Riordan arrays generalize this idea to an upper triangular array that extends infinitely in all directions, that is, now we are indexed over all integers. Riordan arrays are historically defined by a pair of formal power series while extended Riordan arrays are defined by a pair of formal Laurent series. This definition usually encourages constructing these arrays column by column. However, Riordan arrays can also be characterized by using a single element and two types of sequences: An A-sequence that generates rows for the matrix and a Z-sequence that generates the starting column. The A-sequence in particular leads to a natural construction of the array by rows. In this talk we discuss in further detail these A- and Z-sequences.

Abstract: Riordan arrays can be thought of as upper triangular arrays that extend infinitely to the right and downwards; we can consider these as matrices indexed on the non-negative integers. Extended Riordan arrays generalize this idea to an upper triangular array that extends infinitely in all directions, that is, now we are indexed over all integers. Riordan arrays are historically defined by a pair of formal power series while extended Riordan arrays are defined by a pair of formal Laurent series. This definition usually encourages constructing these arrays column by column. However, Riordan arrays can also be characterized by using a single element and two types of sequences: An A-sequence that generates rows for the matrix and a Z-sequence that generates the starting column. The A-sequence in particular leads to a natural construction of the array by rows. In this talk we discuss in further detail these A- and Z-sequences.