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- W3037588995 abstract "We determine the critical exponent and the recurrence function ofcomplementary symmetric Rote sequences. The formulae are expressed in terms ofthe continued fraction expansions associated with the S-adic representations ofthe corresponding standard Sturmian sequences. The results are based on athorough study of return words to bispecial factors of Sturmian sequences.Using the formula for the critical exponent, we describe all complementarysymmetric Rote sequences with the critical exponent less than or equal to 3,and we show that there are uncountably many complementary symmetric Rotesequences with the critical exponent less than the critical exponent of theFibonacci sequence. Our study is motivated by a~conjecture on sequences rich inpalindromes formulated by Baranwal and Shallit. Its recent solution by Curie,Mol, and Rampersad uses two particular complementary symmetric Rote sequences." @default.
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- W3037588995 date "2020-06-06" @default.
- W3037588995 modified "2023-09-26" @default.
- W3037588995 title "Complementary symmetric Rote sequences: the critical exponent and the recurrence function" @default.
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