Fibonacci words in hyperbolic Pascal triangles

Fibonacci words in hyperbolic Pascal triangles AbstractThe hyperbolic Pascal triangle HPT4,q (q ≥ 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In the present study we show that a natural pattern of rows of HPT 4,5 is almost the same as the sequence consisting of every second term of the well-known Fibonacci words. Further, we give a generalization of the Fibonacci words using the hyperbolic Pascal triangles. The geometrical properties of a HPT 4,q imply a graph structure between the finite Fibonacci words. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Universitatis Sapientiae, Mathematica de Gruyter

Fibonacci words in hyperbolic Pascal triangles

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Publisher
De Gruyter Open
Copyright
© 2017 László Németh, published by De Gruyter Open
eISSN
2066-7752
D.O.I.
10.1515/ausm-2017-0025
Publisher site
See Article on Publisher Site

Abstract

AbstractThe hyperbolic Pascal triangle HPT4,q (q ≥ 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In the present study we show that a natural pattern of rows of HPT 4,5 is almost the same as the sequence consisting of every second term of the well-known Fibonacci words. Further, we give a generalization of the Fibonacci words using the hyperbolic Pascal triangles. The geometrical properties of a HPT 4,q imply a graph structure between the finite Fibonacci words.

Journal

Acta Universitatis Sapientiae, Mathematicade Gruyter

Published: Dec 1, 2017

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