Abstract
The k-spectrum of a word is the multiset of its non-contiguous subwords of length k. For given k, how small can n be for a pair of different words of length n to exist, with equal k- spectra? From the Thue-Morse word we find that n is at most 2k. The construction of this paper decreases this upper bound to θ k, where \(\bumpeq\) is the golden ratio; the construction was found, though not published, over thirty years ago. Recently the bound has been further reduced, but remains considerably greater than the greatest known lower bound.
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Milner, R. (2005). The Spectra of Words. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds) Processes, Terms and Cycles: Steps on the Road to Infinity. Lecture Notes in Computer Science, vol 3838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11601548_1
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DOI: https://doi.org/10.1007/11601548_1
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