On some q-Pascal’s like triangles

Toufik Mansour and Matthias Schork
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 21, 2015, Number 4, Pages 64—69
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Authors and affiliations

Toufik Mansour
Department of Mathematics, University of Haifa
31905 Haifa, Israel

Matthias Schork
Camillo-Sitte-Weg 25, 60488 Frankfurt, Germany

Abstract

We consider q-analogs of Pascal’s like triangles, which were studied by Atanassov in a series of papers.

Keywords

  • Pascal triangle
  • Sequence
  • q-binomial coefficient

AMS Classification

  • 11B37

References

  1. Andrews, G. E. (2004) Fibonacci numbers and the Rogers-Ramanujan identities, Fibonacci Quarterly, 42(1), 3–19.
  2. Atanassov, K. T. (2007) On some Pascal’s like triangles. Part 1, Notes on Number Theory and Discrete Mathematics, 13(1), 31–36.
  3. Atanassov, K. T. (2007) On some Pascal’s like triangles. Part 2, Notes on Number Theory and Discrete Mathematics, 13(2), 10–14.
  4. Bondarenko, B. A. (1993) Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs and Applications, The Fibonacci Association.
  5. Carlitz, L. (1974) Fibonacci notes – 3: q-Fibonacci numbers, Fibonacci Quarterly, 12(4), 317–322.
  6. Goldwasser, J., W. Klostermeyer, M. Mays & G. Trapp (1999) The density of ones in Pascal’s rhombus. Discrete Mathematics, 204, 231–236.
  7. Leyendekkers, J. V., A. G. Shannon & J. M. Rybak (2007) Pattern recognition: Modular Rings and Integer Structure. Raffles KvB Monograph No. 9, North Sydney.
  8. Schur, I. (1917) Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbruche, Sitzungsber., Akad. Wissensch. Berlin, Phys.-Math. Klasse, 302–321.

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Cite this paper

APA

Mansour, T. & Schork, M. (2015). On some q-Pascal’s like triangles. Notes on Number Theory and Discrete Mathematics, 21(4), 64-69.

Chicago

Mansour, Toufik and Matthias Schork. “On Some q-Pascal’s Like Triangles.” Notes on Number Theory and Discrete Mathematics 21, no. 4 (2015): 64-69.

MLA

Mansour, Toufik and Matthias Schork. “On Some q-Pascal’s Like Triangles.” Notes on Number Theory and Discrete Mathematics 21.4 (2015): 64-69. Print.

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