On the r-shifted central triangles of a Riordan array

2019/06/04 by Paul Barry, Barry, Paul
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #11C20 #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #Genome Rearrangement Algorithms #Primary 15B36 #Secondary 11B83

paper · pdf · doi:10.48550/arxiv.1906.01328

openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a proper Riordan array with general element a_n,k. We study the one parameter family of matrices whose general elements are given by a_{2n+r, n+k+r}. We show that each such matrix can be factored into a product of a Riordan array and the original Riordan array A, thus exhibiting each element of the family as a Riordan array. We find transition relations between the elements of the family, and examples are given. Lagrange inversion is used as a main tool in the proof of these results.

Citations

• Production Matrices and Riordan Arrays
• The on-line encyclopedia of integer sequences

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