A linear operator approach to succession rules
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.
scientific article; zbMATH DE number 1760985