A linear operator approach to succession rules

Linear Algebra and Its Applications

Volumn 348, Issue 1-3, 2002, Pages 231-246

  Ferrari, Luca ^a   Pinzani, Renzo ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

ECO method; Generating function; Rule operator; Succession rule

Indexed keywords

MATHEMATICAL OPERATORS;

COMBINATORIAL OBJECTS; ECO METHOD; GENERATING FUNCTIONS; LINEAR OPERATORS; RULE OPERATOR; SUCCESSION RULE;

ALGEBRA;

EID: 31244432084     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00584-5     Document Type: Article

References (12)

1. M. Aigner, Catalan-like numbers and determinants, J. Combin. Theory Ser. A 87 (1999) 33-51.
2. C. Banderier, Combinatoire analitique des chemins et des cartes, Ph.D. Thesis, Univ. Paris VI, France, 2001.
3. C. Banderier, M. Bousquet-Mélou, A. Denise, P. Flajolet, D. Gardy, D. Gouyou-Beauchamps, On generating functions of generating trees, in: Proceedings of 11th FPSAC, Barcellona, 1999, pp. 40-52.
4. E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, ECO: a methodology for the enumeration of combinatorial objects, J. Difference Equation Appl. 5 (1999) 435-490.
5. M. Barnabei, A. Brini, G. Nicoletti, Recursive matrices and umbral calculus, J. Algebra 75 (1982) 546-573.
6. F.R.K. Chung, R.L. Graham, V.E. Hoggatt, M. Kleiman, The number of Baxter permutations, J. Combin. Theory Ser. A 24 (1978) 382-394.
7. A. Di Bucchianico, D.E. Loeb, Operator expansion in the derivative and multiplication by x, Integral Transform. Spec. Funct. 4 (1996) 49-68.
8. L. Ferrari, E. Pergola, R. Pinzani, S. Rinaldi, An algebraic characterization of the set of succession rules, Theoret. Comput. Sci. (to appear).
9. D.Merlini, R. Sprugnoli, M.C. Verri, An algebra for proper generating trees, in: Gardy, Mokkadem (Eds.), Trends in Mathematics, Mathematics and Computer Science, Birkhäuser, Berlin, 2000.
10. D. Merlini, M.C. Verri, Generating trees and proper Riordan arrays, Discrete Math. 218 (2000) 167-183.
11. L.W. Shapiro, S. Getu, W.-J. Woan, L.C. Woodson, The Riordan group, Discrete Appl. Math. 34 (1991) 229-239.
12. J. West, Generating trees and forbidden subsequences, Discrete Math. 157 (1996) 363-374.