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- W3048653920 abstract "We study the growth rate of some power-free languages. For any integer $k$ and real $beta>1$, we let $alpha(k,beta)$ be the growth rate of the number of $beta$-free words of a given length over the alphabet ${1,2,ldots, k}$. Shur studied the asymptotic behavior of $alpha(k,beta)$ for $betage2$ as $k$ goes to infinity. He suggested a conjecture regarding the asymptotic behavior of $alpha(k,beta)$ as $k$ goes to infinity when $1<beta<2$. He showed that for $frac{9}{8}lebeta<2$ the asymptotic upper-bound holds of his conjecture holds. We show that the asymptotic lower-bound of his conjecture holds. This implies that the conjecture is true for $frac{9}{8}lebeta<2$." @default.
- W3048653920 created "2020-08-18" @default.
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- W3048653920 date "2020-08-12" @default.
- W3048653920 modified "2023-09-25" @default.
- W3048653920 title "Lower-bounds on the growth of power-free languages over large alphabets" @default.
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