Fibonacci words in hyperbolic Pascal triangles-Reference-Cited by-同舟云学术

Fibonacci words in hyperbolic Pascal triangles

Published:2017-12-01 Issue:2 Volume:9 Page:336-347
ISSN:2066-7752
Container-title:Acta Universitatis Sapientiae, Mathematica
language:en
Short-container-title:

Author:

Németh László¹

Affiliation:

1. Institute of Mathematics , University of Sopron , Hungary

Abstract

Abstract The hyperbolic Pascal triangle HPT 4,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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference8 articles.

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3. [3] G. Fici, Factorizations of the Fibonacci Infinite Word, Journal of Integer Sequences Vol. 18 (2015), 15.9.3.

4. [4] M. Lothaire, Combinatorics on words, Addison-Wesley, Reading, MA, 1983.

5. [5] L. Németh, L. Szalay, Alternating sums in hyperbolic Pascal triangles, Miskolc Mathematical Notes, 17(2) (2016), 989–998.

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