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New bounds on antipowers in words
Information Processing Letters ( IF 0.7 ) Pub Date : 2020-08-17 , DOI: 10.1016/j.ipl.2020.106021
Lukas Fleischer , Samin Riasat , Jeffrey Shallit

Fici et al. defined a word to be a k-power if it is the concatenation of k consecutive identical blocks, and an r-antipower if it is the concatenation of r pairwise distinct blocks of the same size. They defined N(k,r) as the smallest such that every binary word of length contains either a k-power or an r-antipower. In this note we obtain some new upper and lower bounds on N(k,r). We also consider avoiding 3-antipowers and 4-antipowers over larger alphabets, and obtain a lower bound for N(k,5) in the binary case.



中文翻译:

反权力的新界限

Fici等。定义一个字是一个ķ -power如果它的串联ķ连续相同的块,和- [R -antipower如果是的串联- [R相同尺寸的成对不同块。他们定义ñķ[R作为最小的,使得每个长度为ℓ的二进制字都包含k次幂或r次幂。在本说明中,我们获得了一些新的上下界ñķ[R。我们还考虑在较大的字母上避免使用3反幂和4反幂,并为ñķ5 在二进制情况下。

更新日期:2020-09-22
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