<abstract xmlns="http://www.w3.org/1999/xhtml">The hyperbolic Pascal triangle <italic>HPT</italic>4,q (q <italic>≥</italic> 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 <italic>HPT</italic>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 <italic>HPT</italic>4,q imply a graph structure between the finite Fibonacci words.</abstract>

The 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 HPT4,5 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 HPT4,q imply a graph structure between the finite Fibonacci words.

Fibonacci words in hyperbolic Pascal triangles

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Fibonacci words in hyperbolic Pascal triangles"}

The hyperbolic Pascal triangle HPT4,q (q ≥ 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In...

Fibonacci words in hyperbolic Pascal triangles

Published Online: Mar 07, 2018

Page range: 336 - 347

Received: Apr 17, 2017

DOI: https://doi.org/10.1515/ausm-2017-0025

Keywords
hyperbolic Pascal triangle, Fibonacci word

© 2017 László Németh, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fibonacci words in hyperbolic Pascal triangles

Published Online: Mar 07, 2018

Page range: 336 - 347

Received: Apr 17, 2017

DOI: https://doi.org/10.1515/ausm-2017-0025

Keywordshyperbolic Pascal triangle, Fibonacci word

© 2017 László Németh, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
hyperbolic Pascal triangle, Fibonacci word