DOI QR코드

DOI QR Code

SEQUENTIAL PROPERTIES OVER q-COMMUTING ARITHMETIC TABLES

  • Choi, Eunmi (Department of Mathematics Hannam University)
  • 투고 : 2019.05.03
  • 심사 : 2019.10.26
  • 발행 : 2019.11.15

초록

Let C(q) be the q-commuting arithmetic table of (x + y)n with noncommuting variables. We study sequential properties of diagonal sums of C(q) with various q > 0. One of our results shows that each diagonal sum plays like Fibonacci number with some minor conditions.

키워드

과제정보

This work was supported by 2019 Hannam University Research Fund.

참고문헌

  1. M.Braun, An algebraic interpretation of the q-binomial coefficients, International Electronic Journal of Algebra, 6 (2009), 23-30.
  2. W. Guo, Y.J. Lin, Y. Liu, and C. Zhang, A q-analogue of Zhang's binomial coefficient identities, Discrete Math., 309 (2009), 5913-5919. https://doi.org/10.1016/j.disc.2009.04.008
  3. W. Guo and C. Krattenthaler, Some divisibility properties of binomial and q-binomial coefficients, J. Number theory, 135 (2014), 167-184. https://doi.org/10.1016/j.jnt.2013.08.012
  4. M.E. Horn, Pascal Pyramids, Pascal Hyper-Pyramids and a Bilateral Multinomial Theorem, arXiv:0311.035 [math.GM], 2003.
  5. M.E. Horn, Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacob-sthal Numbers, arXiv:0711.4030 [math.GM], 2007.
  6. C.H. Jones, Generalized hockey stick identity and N-dimensional blockwalking, Fibonacci Quarterly, 34 (1994), 280-288.
  7. T.H. Koornwinder, Special functions and q-commuting variables, in Special Functions, q-Series and Related Topics, M. Ismail, D. Masson, M. Rahman (eds.), Fields Institute Communications 14, Amer. Math. Soc. (1997), 131-166.
  8. W. Pauli, The In uence of Archetypal Ideas on the Scientific Theories of Kepler, in: The Interpretation of Nature and the Psyche, Series LI, Pantheon Books, New York (1955), reprint in: W. Pauli: Writings on Physics and Philosophy, C. Enz, K. Meyenn (eds.), Springer, New York (1994), 218-279.

피인용 문헌

  1. Sequential Properties over Negative Pauli Pascal Table vol.2020, 2019, https://doi.org/10.1155/2020/3805462