Double 3-dimensional Riordan arrays and their applications

Abstract

In this paper, we give the group of double 3-dimensional Riordan arrays. Also we examine new sums involving Fibonacci numbers and special numbers, using combinatorial identities and the double 3-dimensional Riordan arrays.

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References

A. T. Benjamin, D. Gaebler and R. Gaebler, A combinatorial approach to hyperharmonic numbers. Integers Electron. J. Combin. Number Theory 3, 1-9, (2003).

G. S. Cheon and S. T. Jin, The group of multi-dimensional Riordan arrays. Linear Algebra and its Applications 524, 263-277, (2017).

D. E. Davenport, L. W. Shapiro and L. C. Woodson The double Riordan group. The Electronic J. of Combin. 18(2), P33, (2012).

A. Gertsch, Generalized harmonic numbers. J. Number Theory 324, 7-10, (1997).

J. M. Santmyer, A Stirling like sequence of rational numbers. Discrete Mathematics 171(1-3), 229-235, (1997).

L. W. Shapiro, S. Getu, W. Woan and L. C. Woodson, The Riordan Group, Discrete Applied Mathematics 34, 229-239, (1991).

L. W. Shapiro, Bijections and the Riordan group. Theoret. Comput. Sci. 307, 403-413, (2003).

A. M. G. Solo, Multidimensional matrix mathematics: Multidimensional matrix equality, addition subtraction and multiplication, Part 2 of 6 in:proceeding of the world congress on engineering 2010, vol III, 1829-1833, (2010).

T. X. He, Sequences characterizations of double Riordan arrays and their compressions. Linear Algebra and Its Applications 549(15), 176-202, (2018).

C. Wang, P. Miska and I. Mez˝o, The r−derangement numbers. Discrete Math. 340, 1681-1692, (2017).

Published
2025-06-11
Section
Articles