Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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A RECURRENCE RELATION ASSOCIATED WITH UNIT-PRIMITIVE MATRICES

  • Byeong-Gil Choe (Department of Mathematics, Chonnam National University) ;
  • Hyeong-Kwan Ju (Department of Mathematics, Chonnam National University)
  • Received : 2023.08.01
  • Accepted : 2023.10.06
  • Published : 2024.03.20
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Abstract

In this paper we obtained several properties that the characteristic polynomial of the unit-primitive matrix satisfies. In addition, using these properties we have shown that the recurrence relation given as in the formula (1) is true. In fact, Xin and Zhong ([4]) showed it earlier. However, we provide a simpler method here.

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References

  1. S. J. Cyvin and I. Gutman, Kekule Structures in Benzenoids Hydrocarbons, Lecture Notes in Chemistry 46, 142-144, Springer, New York, 1988. https://doi.org/10.1007/978-3-662-00892-8
  2. H.-K. Ju, On the sequence generated by a certain type of matrices, Honam Math. J. 39 (2017), no. 4, 665-675.
  3. The On-Line Encyclopedia of Integer Sequences, available at https://oeis.org.
  4. G. Xin and Y. Zhong, Proving some conjectures on Kekule numbers for certain Benzenoids by using Chebyshev polynomials, to appera in Advances in Applied Math. 415 (2023).