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arXiv · 1703.01588

Fibonacci words in hyperbolic Pascal triangles

László Németh
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Abstract

The hyperbolic Pascal triangle ${\cal HPT}_{4,q}$ $(q\ge5)$ 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 ${\cal HPT}_{4,5}$ 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 ${\cal HPT}_{4,q}$ imply a graph structure between the finite Fibonacci words.

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László Németh. 2017-03-05. Fibonacci words in hyperbolic Pascal triangles. https://arxiv.org/abs/1703.01588

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