On some alternative characterizations of Riordan Arrays

Canadian Journal of Mathematics

Volumn 49, Issue 2, 1997, Pages 301-320

  Merlini, Donatella ^a   Rogers, Douglas G ^b   Sprugnoli, Renzo ^a   Verri, M Cecilia ^a  

^a Dipartimento di Sistemi e Informatica   (Italy)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031508649     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-1997-015-x     Document Type: Article

References (24)

1. M. Barnabei, A. Brini, and G. Nicoletti, Recursive matrices and umbral calculus, J. Algebra 75(1982), 546-573.
2. R. D. Fray and D. P. Roselle, Weighted lattice paths, Pacific J. Math. 37(1971), 85-96.
3. _, On weighted lattice paths, J. Combin. Theory Ser. A 14(1973), 21-29.
4. I. M. Gessel, A factorization for formal Laurent series and lattice path enumeration, J. Combin. Theory Ser. A 28(1980), 321-337.
5. J. R. Goldman and T. Sundquist, Lattice path enumeration by formal schema, Adv. in Appl. Math. 13(1992), 216-251.
6. E. Goodman and T. V. Narayana, Lattice paths with diagonal steps, Canad. Math. Bull. 12(1969), 847-855.
7. I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley & Sons, 1983.
8. B. R. Handa and S. G. Mohanty, Higher dimensional lattice paths with diagonal steps, Discrete Math. 15(1976), 137-140.
9. P. Henrici, Applied and Computational Complex Analysis, I, Wiley, New York, 1988.
10. J. Labelle, Languages de Dyck généralisés, Ann. Sci. Math. Québec (1) 17(1993), 53-64.
11. _, On pairs of non-crossing generalized Dyck paths, J. Statist. Plann. Inference 34(1993), 209-217.
12. _, Lattice paths with or without horizontal steps, Congr. Numer. 101(1994), 233-241.
13. J. Labelle and Y. Yeh, Dyck paths of knight moves, Discrete Appl. Math. 24(1989), 213-221.
14. _, Generalized Dyck paths, Discrete Math. 82(1990), 1-6.
15. D. Merlini, D. G. Rogers, R. Sprugnoli, and M. C. Verri, On some alternative characterizations of Riordan arrays, Technical Report 14, Dipartimento di Sistemi e Informatica, Università di Firenze, 1995.
16. D. Merlini, R. Sprugnoli, and M. C. Verri, Algebraic and combinatorial properties of simple, coloured walks. In: Proceedings of CAAP'94, Lecture Notes in Comp. Sci. 787, 218-233, 1994.
17. S. G. Mohanty and B. R. Handa, On lattice paths with several diagonal steps, Canad. Math. Bull. 11(1968), 537-545.
18. L. Moser and W. Zayachkowski, Lattice paths with diagonal steps, Scripta Math. 26(1963), 223-229.
19. D. G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. 22(1978), 301-310.
20. D. G. Rogers and L. W. Shapiro, Deques, trees and lattice paths, Lecture Notes in Math. 884(1981), 292-303.
21. V. K. Rohatgi, On lattice paths with diagonals steps, Canad. Math. Bull. 7(1964), 470-472.
22. L. Shapiro, A survey of the Riordan Group, Proc. Amer. Math. Soc., Richmond, Virginia, 1994.
23. L. V. Shapiro, S. Getu, W.-J. Woan, and L. Woodson, The Riordan group, Discrete Appl. Math. 34(1991), 229-239.
24. R. Sprugnoli, Riordan arrays and combinatorial sums, Discrete Math. 132(1994), 267-290.