Hyperbolic Pascal Simplex

In this article we introduce a new geometric object called hyperbolic Pascal simplex. This new

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  • [1] Anatriello, G. and Vincenzi, G., Tribonacci-like sequences and generalized Pascal’s pyramids. Internat. J. Math. Ed. Sci. Tech., 45 (2014), 1220-1232.
  • [2] Belbachir, H., Németh, L. and Szalay, L., Hyperbolic Pascal triangles. Appl. Math. Comp., 273 (2016), 453-464.
  • [3] Belbachir, H. and Szalay, L., On the arithmetic triangles. ˘ Siauliai Math. Sem., 9 (2014), 15-26.
  • [4] Bondarenko, B. A., Generalized Pascal triangles and pyramids, their fractals, graphs, and applications. Translated from the Russian by Bollinger, R. C. (English) Santa Clara, CA: The Fibonacci Association, vii, 253 p. 1993. www.fq.math.ca/pascal.html
  • [5] Coxeter, H. S. M., Regular honeycombs in hyperbolic space. Proc. Int. Congress Math., Amsterdam, Vol. III. (1954), 155-169.
  • [6] Fiorenza, A. and Vincenzi, G., Limit of ratio of consecutive terms for general order-k linear homogeneous recurrences with constant coefficients. Chaos, Solitons & Fractals, 44 (2011), 147-152.
  • [7] Fiorenza, A. and Vincenzi, G., From Fibonacci Sequence to the Golden Ratio. Journal of Mathematics, (2013), Article ID 204674, 3 pages. [8] Harris, J, M., Hirst, J. L. and Mossinghoff, M. J., Combinatorics and Graph Theory. Springer, 2008.
  • [9] Németh, L. and Szalay, L., Alternating sums in hyperbolic Pascal triangles. Miskolc Mathematical Notes, 17 (2016), no. 2, 989-998.
  • [10] Németh, L. – Szalay, L., Recurrence sequences in the hyperbolic Pascal triangle corresponding to the regular mosaic f4; 5g. Annales Mathematicae et Informaticae, 46 (2016), 165–173.
  • [11] Németh, L. and Szalay, L., Power sums in hyperbolic Pascal triangles. Analele Univ. “Ovidius”, Math Series., (2018) (to appear).
  • [12] Németh, L., Fibonacci words in hyperbolic Pascal triangles. Acta Universitatis Sapientiae Mathematica, 9 (2017) no. 2, (to appear).
  • [13] Németh, L. On the hyperbolic Pascal pyramid. Beitr Algebra Geom., 57 (2016), 913–927.
  • [14] Németh, L., On the 4-dimensional hypercube mosaics. Publ. Math. Debrecen, 70 (2007), no. 3–4, 291–305.
  • [15] Németh, L., Pascal pyramid in space H2R. Mathematical Communications, 22 (2017), 211-225.
  • [16] Németh, L., The growing ration of hyperbolic regular mosaics with bounded cell, Armenian Journal of Mathematics, 9 (2017), 1-19.
  • [17] Siani, S. and Vincenzi, G., Fibonacci-like sequences and generalized Pascal’s triangles. Internat. J. Math. Ed. Sci. Tech., 45 (2014), 609-614.