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On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices

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  • Kilic, E.
  • Stakhov, A.P.

Abstract

In this paper we consider certain generalizations of the well-known Fibonacci and Lucas numbers, the generalized Fibonacci and Lucas p-numbers. We give relationships between the generalized Fibonacci p-numbers, Fp(n), and their sums, ∑i=1nFp(i), and the 1-factors of a class of bipartite graphs. Further we determine certain matrices whose permanents generate the Lucas p-numbers and their sums.

Suggested Citation

  • Kilic, E. & Stakhov, A.P., 2009. "On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2210-2221.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2210-2221
    DOI: 10.1016/j.chaos.2007.10.007
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    References listed on IDEAS

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    1. Marek-Crnjac, L., 2006. "The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1113-1118.
    2. El Naschie, M.S., 2007. "From symmetry to particles," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 427-430.
    3. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    4. El Naschie, M.S., 2007. "On the topological ground state of E-infinity spacetime and the super string connection," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 468-470.
    5. Stakhov, Alexey & Rozin, Boris, 2006. "Theory of Binet formulas for Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1162-1177.
    6. Stakhov, A.P., 2005. "The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 263-289.
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    Cited by:

    1. Şahin, Adem & Ramírez, José L., 2016. "Determinantal and permanental representations of convolved Lucas polynomials," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 314-322.
    2. Natalia Bednarz, 2021. "On ( k , p )-Fibonacci Numbers," Mathematics, MDPI, vol. 9(7), pages 1-13, March.
    3. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.
    4. Anetta Szynal-Liana & Iwona Włoch, 2020. "On Special Spacelike Hybrid Numbers," Mathematics, MDPI, vol. 8(10), pages 1-10, October.

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