Hyperbolic Pascal triangles
Hacene Belbachir, László Németh, László Szalay
(Submitted on 5 Mar 2015)
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 describe precisely 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 appearence of some binary recurrences in a fixed hyperbolic triangle are investigated.
Comments: 18 pages, 15 figures
Subjects: History and Overview (math.HO); Combinatorics (math.CO)
MSC classes: 11B99, 05A10
Cite as: arXiv:1503.02569 [math.HO]
(or arXiv:1503.02569v1 [math.HO] for this version)
Submission history
From: Laszlo Nemeth [view email]
[v1] Thu, 5 Mar 2015 09:00:18 GMT (5635kb,D)
FREE PDF GRATIS: ArXiv
