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Hyperbolic Pascal triangles

Author

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  • Belbachir, Hacène
  • Németh, László
  • Szalay, László

Abstract

In this paper, we introduce a new generalization of Pascal’s triangle. The new object is called the hyperbolic Pascal triangle since the mathematical background goes back to regular mosaics on the hyperbolic plane. We precisely describe the procedure of how to obtain a given type of hyperbolic Pascal triangle from a mosaic. Then we study certain quantitative properties such as the number, the sum, and the alternating sum of the elements of a row. Moreover, the pattern of the rows, and the appearance of some binary recurrences in a fixed hyperbolic triangle are investigated.

Suggested Citation

  • Belbachir, Hacène & Németh, László & Szalay, László, 2016. "Hyperbolic Pascal triangles," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 453-464.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:453-464
    DOI: 10.1016/j.amc.2015.10.001
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    Cited by:

    1. Anatriello, Giuseppina & Németh, László & Vincenzi, Giovanni, 2022. "Generalized Pascal’s triangles and associated k-Padovan-like sequences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 278-290.

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