Fibonacci words in hyperbolic Pascal triangles

2017/03/05 by Németh, László
#05B30 #11B39 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL)

paper · doi:10.48550/arxiv.1703.01588

Abstract

The hyperbolic Pascal triangle \cal 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 \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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