The Sheffer group and the Riordan group

Discrete Applied Mathematics

Volumn 155, Issue 15, 2007, Pages 1895-1909

  He, Tian Xiao ^a   Hsu, Leetsch C ^b   Shiue, Peter J S ^c  

^a ILLINOIS WESLEYAN UNIVERSITY   (United States)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^c UNIVERSITY OF NEVADA   (United States)

Author keywords

Formal power series; Generalized weighted Stirling numbers; Riodan array; Riordan group; Sheffer group; Sheffer type differential operators; Sheffer type polynomials

Indexed keywords

DIFFERENTIAL EQUATIONS; THEOREM PROVING;

FORMAL POWER SERIES; SHEFFER GROUP; SHEFFER-TYPE DIFFERENTIAL OPERATORS; SHEFFER-TYPE POLYNOMIALS;

POLYNOMIALS;

EID: 34547751305     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2007.04.006     Document Type: Article

References (26)

1. Boas R.P., and Buck R.C. Polynomial Expansions of Analytic Functions (1964), Springer, New York
2. Broder A.Z. The r-Stirling numbers. Discrete Math. 49 (1984) 241-259
3. Cameron N.T., and Nkwanta A. On some (pseudo) involutions in the Riordan group. J. Integer Seq. 8 3 (2005) (Article 05.3.7, 16pp., electronic)
4. Carlitz L. Weighted Stirling numbers-I. II, Fibonacci Quart. 18 (1980) 147-162, 242-257
5. Comtet L. Advanced Combinatorics (1974), Reidel, Dordrecht (Chapters 1 and 3)
6. Constantine G.M., and Savits T.H. A multivariate Faa di Bruno formula with applications. Trans. Amer. Math. Soc. 348 2 (1996) 503-520
7. He T.X., Hsu L.C., and Shiue P.J.-S. Multivariate expansion associated with Sheffer-type polynomials and operators. Bull. Inst. Math. Acad. Sin. (N.S.) 1 4 (2006) 451-473
8. Howard F. Degenerate weighted Stirling numbers. Discrete Math. 57 (1985) 45-58
9. Hsu L.C. Generalized Stirling number pairs associated with inverse relations. Fibonacci Quart. 25 (1987) 346-351
10. Hsu L.C. Theory and application of general Stirling number pairs. J. Math. Res. Exposition 9 2 (1989) 211-220
11. Hsu L.C., and Shiue P.J.-S. A unified approach to generalized Stirling numbers. Adv. Appl. Math. 20 3 (1998) 366-384
12. Hsu L.C., and Shiue P.J.-S. Cycle indicators and special functions. Ann. Comb. 5 (2001) 179-196
13. Jordan C. Calculus of Finite Differences (1965), Chelsea, New York
14. Liu G. Higher-order multivariable Euler's polynomial and higher-order multivariable Bernoulli's polynomial. Appl. Math. Mech. 19 9 (1998) 895-906 (English Ed.) Translated from Appl. Math. Mech. 19 (9) (1998) 827-836 (Chinese)
15. A. Nkwanta, A Riordan matrix approach to unifying a selected class of combinatorial arrays, in: Proceedings of the 34th Southeastern International Conference on Combinatorics Graph Theory and Computing, Congr. Numer. 160 (2003) 33-45.
16. A. Nkwanta, N. Knox, A note on Riordan matrices, African Americans in Mathematics, vol. II, Houston, TX, 1998, pp. 99-107, Contemp. Math. 252 (1999).
17. Remmel J.B., and Wachs M.L. Rook theory, generalized Stirling numbers and (p, q) analogues. Electron. J. Combin. 11 1 (2004) (Research Paper 84, 48pp., electronic)
18. Roman S. The Umbral Calculus (1984), Academic Press, New York
19. S. Roman, G.-C. Rota, The Umbral calculus, Adv. Math. (1978) 95-188.
20. Rota G.-C. Finite Operator Calculus (1975), Academic Press, New York
21. Schur I. On Faber polynomials. Amer. J. Math. 67 (1945) 33-41
22. Shapiro L. Bijections and the Riordan group. Theoret. Comput. Sci. 307 (2003) 403-413
23. Shapiro L., Getu S., Woan W.-J., and Woodson L.C. The Riordan group. Discrete Appl. Math. 34 (1991) 229-239
24. Sprugnoli R. Riordan arrays and combinatorial sums. Discrete Math. 132 (1994) 267-290
25. Sprugnoli R. Riordan arrays and the Abel-Gould identity. Discrete Math. 142 (1995) 213-233
26. Zhao X., and Wang T. Some identities related to reciprocal functions. Discrete Math. 265 (2003) 323-335