A linear operator approach to succession rules
type: Item
instance of: scholarly article
title: A linear operator approach to succession rules
zbMATH Open document ID: 1003.05007
DOI: 10.1016/S0024-3795(01)00584-5
author: L. Ferrari
author: R. Pinzani
published in: Linear Algebra and its Applications
publication date: 2002-06-27T00:00:00Z
review text: Among the methods commonly applied in enumerative combinatorics to count combinatorial structures, especially with some restrictive conditions, the enumeration of combinatorial objects (ECO) method is a technique widely used. See, e.g., \textit{E. Barcucci}, \textit{A. Del Lungo}, \textit{E. Pergola} and \textit{R. Pinzani} [J. Difference Equ. Appl. 5, 435-490 (1999; Zbl 0944.05005)]. The authors of the present paper give an algebraic version of the ECO method, and of succession rules in general, by means of linear operators. Then they translate some known results about the relationship between ECO-systems and generating functions into their present language. Finally, they deal with the problem of standard form for succession rules, giving a general solution, which is a compact expression for the desired standard form.
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 1760985
zbMATH Keywords: enumerative combinatorics
zbMATH Keywords: enumeration of combinatorial objects
zbMATH Keywords: generating functions
reviewed by: Andreas N. Philippou
MaRDI profile type: Publication
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cites work: ECO:a methodology for the enumeration of combinatorial objects
cites work: Recursive matrices and umbral calculus
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cites work: An algebraic characterization of the set of succession rules
cites work: Q4524576
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description: scientific article; zbMATH DE number 1760985