대한수학회지 (Journal of the Korean Mathematical Society)

  • 제42권4호
  • /
  • Pages.761-771
  • /
  • 2005
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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(±1)-INVARIANT SEQUENCES AND TRUNCATED FIBONACCI SEQUENCES OF THE SECOND KIND

  • CHOI GYOUNG-SIK (Department of Mathematics Education Kyungpook University) ;
  • HWANG SUK-GEUN (Department of Mathematics Education Kyungpook University) ;
  • KIM IK-PYO (Department of Mathematics Education Kyungpook University)
  • 발행 : 2005.07.01
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초록

In this paper we present another characterization of (${\pm}1$)-invariant sequences. We also introduce truncated Fibonacci and Lucas sequences of the second kind and show that a sequence $x\;{\in}\;R^{\infty}$ is (-1)-invariant(l-invariant resp.) if and only if $D[_x^0]$ is perpendicular to every truncated Fibonacci(truncated Lucas resp.) sequence of the second kind where $$D=diag((-1)^0,\; (-1)^1,\;(-1)^2,{\ldots})$$.

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참고문헌

  1. G.-S. Choi, S.-G. Hwang, and I.-P. Kim, $({\pm}1)$-Invariant sequences and truncated Fibonacci sequences, submitted
  2. G.-Y. Lee, k-Lucas numbers and associated bipartite graphs, Linear Algebra Appl. 320 (2000), 51-61 https://doi.org/10.1016/S0024-3795(00)00204-4
  3. G.-Y. Lee, S.-G. Lee and H.-G. Shin, On the k-th generalized Fibonacci matrix Qk, Linear Algebra Appl. 251 (1997), 73-88 https://doi.org/10.1016/0024-3795(95)00553-6
  4. Z.-H. Sun, Invariant sequences under binomial transformation, Fibonacci Quart. 39 (2001), 324-333