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Independently, Pirillo and Varricchio, Halbeisen and Hungerbühler and Freedman considered the following problem, open since 1992: Does there exist an infinite word w over a finite subset of Z such that w contains no two consecutive blocks of the same length and sum? We consider some variations on this problem in the light of van der Waerden's theorem on… (More)

- Yu-Hin Au
- 2009

We present a simple algorithm that generate a De Bruijn sequence the set of primitive words of any given length over any alphabet. We also show that the shortest sequence that contains all squares of length 2n over an alphabet of size k has length between 2k n and (2 + 1 k)k n .

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