East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

ON k SLOPE DIAGONAL SUMS OF q-COMMUTING TABLE AND NONZERO PAULI TABLE

  • Received : 2019.09.20
  • Accepted : 2020.05.26
  • Published : 2020.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

We explore the Pauli table C(-1) and nonzero Pauli table W. Recurrence rules and interrelationships of any k slope diagonal sums over C(-1) and W are studied in connection with diagonal sums of the Pascal table C(1). Since diagonal sums of C(1) are Fibonacci numbers, any k slope diagonal sums over C(-1) and W are explained by Fibonacci numbers.

Keywords

References

  1. M.E. Horn, Pascal pyramids, Pascal hyper-pyramids and a bilateral multinomial theorem, arXiv:0311.035 [math.GM], 2003.
  2. M.E. Horn, Pauli Pascal pyramids, Pauli Fibonacci numbers, and Pauli Jacobsthal numbers, arXiv:0711.4030 [math.GM], 2007.
  3. E. Kilic, The Binet formula, sums and representations of generalized Fibonacci p-numbers, European J. Combinatorics (2008), 701 - 711.
  4. 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, AMS. (1997), 131 - 166.
  5. W. Pauli, The influence of archetypal ideas on scientific theories of Kepler, in: Interpretation of nature and the psyche, Series LI, Pantheon Books (1955), reprint in: W. Pauli: Writings on physics and philosophy, C. Enz, K. Meyenn (eds.), Springer (1994), 218 - 279.
  6. A. Stakhov, B. Rozin, Theory of Binet formulas for Fibonacci and Lucas p-numbers, Chaos Solitons Fractals 27 (2006), 1162 - 1177. https://doi.org/10.1016/j.chaos.2005.04.106