Presentation	2007-04-26 Repetitions in the infinite n-bonacci word Takahito SASAKI, Tsugutoyo OSAKI, Akira ISHINO, Ayumi SHINOHARA,
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Abstract(in English)	The Fibonacci word F_m is defined as the concatenation of the preceding two Fibonacci words F_ and F_. We generalize it to the n-bonacci word as the concatenation of the preceding n words. We consider the structure of the subword repetitions in the n-bonacci word. In Fibonacci word (n=2), the maximal repetition of the subword is known to be less than 2+Φ, where Φ=(1+√<5>)/2 is the golden ratio. We give a general result for any n≧2. We prove that the maximal repetition of the finite k-th n-bonacci word in the infinite n-bonacci word converges to 2+1/(Φ^<(n)>-1) as k → ∞, and it approaches to 3 as n → ∞, and it approaches to 3 as n → ∞, where Φ^<(n)> is the n-bonacci constant and Φ^<(2)>=Φ.
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Keyword(in English)	Fibonacci number / Fibonacci word / repetition / golden ratio
Paper #	COMP2007-8
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Conference Information
Committee	COMP
Conference Date	2007/4/19(1days)
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Registration To	Theoretical Foundations of Computing (COMP)
Language	JPN
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	Repetitions in the infinite n-bonacci word
Sub Title (in English)
Keyword(1)	Fibonacci number
Keyword(2)	Fibonacci word
Keyword(3)	repetition
Keyword(4)	golden ratio
1st Author's Name	Takahito SASAKI
1st Author's Affiliation	Department of System Information Sciences, GSIS, Tohoku University()
2nd Author's Name	Tsugutoyo OSAKI
2nd Author's Affiliation	Department of System Information Sciences, GSIS, Tohoku University
3rd Author's Name	Akira ISHINO
3rd Author's Affiliation	Department of System Information Sciences, GSIS, Tohoku University
4th Author's Name	Ayumi SHINOHARA
4th Author's Affiliation	Department of System Information Sciences, GSIS, Tohoku University
Date	2007-04-26
Paper #	COMP2007-8
Volume (vol)	vol.107
Number (no)	24
Page	pp.pp.-
#Pages	7
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