Abstract
In this paper we introduce a system of well-defined operations on the set of succession rules. These operations allow us to tackle combinatorial enumeration problems simply by using succession rules instead of generating functions. Finally we suggest several open problems the solution of which should lead to an algebraic characterization of the set of succession rules.
This work was partially supported by MURST project: Modelli di calcolo innovativi: metodi sintattici e combinatori
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Banderier, M. Bousquet-Mélou, A. Denise, P. Flajolet, D. Gardy and D. Gouyou-Beauchamps, On generating functions of generating trees, Proceedings of 11th FPSAC, (1999) 40–52.
S. Corteel, Problèmes énumératifs issus de 1’Informatique, de la Physique et de la Combinatorie, Phd Thesis, Université de Paris-Sud, 6082, (2000).
E. Barcucci, A. Del Lungo, A. Frosini, S. Rinaldi, From rational functions to regular languages, Proceedings of 12th FPSAC, Moscow (2000).
E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, ECO: a methodology for the Enumeration of Combinatorial Objects, Journal of Difference Equations and Applications, Vol.5 (1999) 435–490.
E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, Some combinatorial interpretations of q-analogs of Schröder numbers, Annals of Combinatorics, 3 (1999) 173–192.
F. R. K. Chung, R. L. Graham, V. E. Hoggatt, M. Kleimann, The number of Baxter permutations, J. Combin. Theory Ser. A,24 (1978) 382–394.
D. Merlini, C. Verri, Generating trees and proper Riordan Arrays, Discrete Mathematics, 218 (2000) 107–122.
E. Pergola, R. Pinzani, S. Rinaldi, ECO-Approximation of algebraic functions, Proceedings of 12th FPSAC,Moscow (2000).
A. Salomaa and M. Soittola, Automata-theoretic aspects of formal power series, Springer-Verlag, New York, (1978).
N. J. A. Sloane and S. Plouffe, The encyclopedia of integer sequences, Academic press, (1996).
J. West, Generating trees and the Catalan and Schröder numbers, Discrete Mathematics,146 (1995) 247–262.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Basel AG
About this paper
Cite this paper
Pergola, E., Pinzani, R., Rinaldi, S. (2000). A set of well-defined operations on succession rules. In: Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8405-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8405-1_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9553-8
Online ISBN: 978-3-0348-8405-1
eBook Packages: Springer Book Archive