Centralizers of the Riordan Group

Tian-Xiao He () and Yuanziyi Zhang
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Tian-Xiao He: Illinois Wesleyan University
Yuanziyi Zhang: University of Illinois at Urbana-Champaign

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 1058-1072

Abstract: Abstract In this paper, we discuss centralizers in the Riordan group. We will see that Faà di Bruno’s formula is an application of the Fundamental Theorem of Riordan arrays. Then the composition group of formal power series in $${{{\mathcal {F}}}}_1$$ F 1 is studied to construct the centralizers of Bell type and Lagrange type Riordan arrays. Our tools are the A-sequences of Riordan arrays and Faà di Bruno’s formula. Some combinatorial explanation and discussion about related algebraic topics are also given.

Keywords: Centralizer; Riordan group; Formal power series; Generalized Riordan array; Bell polynomial; A-sequence; Faà di Bruno’s formula; Fundamental theorem of Riordan arrays; Bell type Riordan arrays; Lagrange type Riordan arrays; Generating function; 15A30; 08A05; 05A05; 05A15; 05E15; 05E18 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-022-00218-9

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