Urszula BEDNARZ, Malgorzata WOLOWIEC MUSIAL

On a new generalization of telephone numbers

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

In this paper we introduce a new generalization of telephone numbers. We give the generating function,direct formulae, and matrix generators for these numbers. Moreover, we present their interpretations and we prove someproperties of these numbers connected with congruences.

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[1] Bednarz U, Włoch I. Fibonacci and telephone numbers in extremal trees. Discussiones Mathematicae Graph Theory 2018; 28: 121-133.
[2] Bednarz U, Włoch I, Wołowiec-Musiał M. Total graph interpretation of numbers of the Fibonacci type. Journal of Applied Mathematics 2015; 2015: 837917.
[3] Beissinger JS. Similar constructions for Young tableaux and involutions, and their applications to shiftable tableaux. Discrete Mathematics 1987; 67: 149-163.
[4] Cahill ND, Narayan DA. Fibonacci and Lucas numbers as tridiagonal matrix determinants. Fibonacci Quarterly 2004; 42 (3): 216-221.
[5] Chowla S, Herstein IN, Moore WK. On recursions connected with symmetric groups I. Canadian Journal of Mathematics 1951; 3: 328-334.
[6] Kiliç E. The generalized order-k-Fibonacci-Pell sequence by matrix methods. Journal of Computational and Applied Mathematics 2007; 209: 133-145.
[7] Kiliç E, Tasci D. On the generalized Fibonacci and Pell sequences by Hessenberg matrices. Ars Combinatoria 2010; 94: 161-174.
[8] Knuth DE. The Art of Computer Programming, Vol. 3. Boston, MA, USA: Addison-Wesley, 1973.
[9] Moser L, Wyman M. On solutions of xd = 1 in symmetric groups. Canadian Journal of Mathematics 1955; 7: 159-168.
[10] Riordan J. Introduction to Combinatorial Analysis. Mineola, NY, USA: Dover, 2002.
[11] Tichy R, Wagner S. Extremal problems for topological indices in combinatorial chemistry. Journal of Computational Biology 2005; 12 (7): 1004-1013.
[12] Włoch A, Wołowiec-Musiał M. On generalized telephone number, their interpretations and matrix generators. Utilitas Mathematica 2017; 105: 31-39.