TY - JOUR
T1 - On the halves of a Riordan array and their antecedents
AU - Barry, Paul
N1 - Funding Information:
The author completed this article while a guest at the Applied Algebra and Optimization Research Center (AORC) of Sungkyunkwan University, Suwon, South Korea. He gratefully acknowledges their hospitality.
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - Every Riordan array has what we call a horizontal half and a vertical half. These halves of a Riordan array have been studied separately before. Here, we place them in a common context, showing that one may be obtained from the other. Using them, we provide a canonical factorization of elements of the associated or Lagrange subgroup of the Riordan group. The vertical half matrix is shown to be an element of the hitting-time group. We also ask and answer the question: given a Riordan array, when is it the half (either horizontal of vertical) of a Riordan array?
AB - Every Riordan array has what we call a horizontal half and a vertical half. These halves of a Riordan array have been studied separately before. Here, we place them in a common context, showing that one may be obtained from the other. Using them, we provide a canonical factorization of elements of the associated or Lagrange subgroup of the Riordan group. The vertical half matrix is shown to be an element of the hitting-time group. We also ask and answer the question: given a Riordan array, when is it the half (either horizontal of vertical) of a Riordan array?
KW - Central coefficients
KW - Lagrange inversion
KW - Riordan array
KW - Riordan group
UR - http://www.scopus.com/inward/record.url?scp=85070251343&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2019.07.035
DO - 10.1016/j.laa.2019.07.035
M3 - Article
AN - SCOPUS:85070251343
VL - 582
SP - 114
EP - 137
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
ER -