A Class of Formal Operators for Combinatorial Identities and its Application
In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.
<p>[1] Ch. Jordan, Calculus of Finite Differences, Chelsea Publishing Co. New
York, 1970, pp. 66-192.
[2] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Co., Dordrecht,
1974, pp. 169-174.
[3] H. S. Wilf, Generatingfunctionology, Academic Press, New York, 1990,
pp. 48-96.
[4] R. Mullin snd G.-C. ROTA, On the foundations of combinatorial
theory: III. Theory of binomial enumeration, in: Graph Theory and its
Applications, New York and London, 1965, pp. 156-210.
[5] T. X. He, L. C. Hsu, and P.J. S. Shiue, Symbolization of generating functions,
an qpplication of Mullin-Rota’s theory of binomial enumeration,
Comp. Math. with Applications, 54 (2007), pp. 664-678.
[6] G.P.EGORYCHEV, Integral Representation and the Computation of
Combinatorial Sums. American Mathematical Society Providence
RhodeIsLand, 1984, pp. 68-90.</p>
<p>[1] Ch. Jordan, Calculus of Finite Differences, Chelsea Publishing Co. New
York, 1970, pp. 66-192.
[2] L. Comtet, Advanced Combinatorics, D. Reidel Publishing Co., Dordrecht,
1974, pp. 169-174.
[3] H. S. Wilf, Generatingfunctionology, Academic Press, New York, 1990,
pp. 48-96.
[4] R. Mullin snd G.-C. ROTA, On the foundations of combinatorial
theory: III. Theory of binomial enumeration, in: Graph Theory and its
Applications, New York and London, 1965, pp. 156-210.
[5] T. X. He, L. C. Hsu, and P.J. S. Shiue, Symbolization of generating functions,
an qpplication of Mullin-Rota’s theory of binomial enumeration,
Comp. Math. with Applications, 54 (2007), pp. 664-678.
[6] G.P.EGORYCHEV, Integral Representation and the Computation of
Combinatorial Sums. American Mathematical Society Providence
RhodeIsLand, 1984, pp. 68-90.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65136", author = "Ruigang Zhang and Wuyungaowa and Xingchen Ma", title = "A Class of Formal Operators for Combinatorial Identities and its Application", abstract = "In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.
", keywords = "Generating functions, operators sequence group, Riordan arrays, R. G operator group, combinatorial identities.", volume = "7", number = "3", pages = "426-5", }