Abstract
An \(\alpha \)-gapped palindromic factor of a word is a factor of the form \(uv\overline{u}\), where \(\overline{u}\) is the reversal of u and where \(|uv|\le \alpha |u|\) for some fixed \(\alpha \ge 1\). We give an asymptotic estimate of the expected number of distinct palindromic factors in a random word for a memoryless source, where each letter is generated independently from the other, according to some fixed probability distribution on the alphabet.
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Notes
- 1.
The reversal of \(u=u_1\cdots u_n\) is \(\overline{u}=u_n\cdots u_1\).
- 2.
The case where some coordinates are zero is covered by setting \(x\log x=0\) for \(x=0\).
- 3.
We disregard rounding errors in lengths; properly dealing with them by means of integer parts would only yield clumsier notations without changing the asymptotic results.
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Duchon, P., Nicaud, C. (2018). On the Expected Number of Distinct Gapped Palindromic Factors. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_14
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DOI: https://doi.org/10.1007/978-3-319-94667-2_14
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