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- W2563726981 abstract "We investigate the asymptotic growth of the maximal number (mathsf{powers }_{alpha }(n)) of different (alpha )-powers (strings (w) with a period (|w|/alpha )) in an edge-labeled unrooted tree of size (n). The number of different powers in trees behaves much unlike in strings. In a previous work (CPM, 2012) it was proved that the number of different squares in a tree is (mathsf{powers }_2(n) = varTheta (n^{4/3})). We extend this result and analyze other powers. We show that there are phase-transition thresholds:1.(mathsf{powers }_{alpha }(n);=;varTheta (n^2)) for (alpha <2);2.(mathsf{powers }_{alpha }(n);=; varTheta (n^{4/3})) for (2le alpha <3);3.(mathsf{powers }_{alpha }(n);=; {mathcal {O}}(n log n)) for (3le alpha <4);4.(mathsf{powers }_{alpha }(n);=; varTheta (n)) for (4le alpha )." @default.
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- W2563726981 date "2017-01-03" @default.
- W2563726981 modified "2023-10-17" @default.
- W2563726981 title "String Powers in Trees" @default.
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- W2563726981 doi "https://doi.org/10.1007/s00453-016-0271-3" @default.
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