Abstract
We introduce the new concept of “formula with reversal”. We show some simple formulas with reversal that have high index and we give a partial characterization of unavoidable formulas with reversal.
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References
Baker, K., McNulty, G., Taylor, W.: Growth problems for avoidable words. Theoret. Comput. Sci. 69, 319–345 (1989)
Bean, D.R., Ehrenfeucht, A., McNulty, G.F.: Avoidable patterns in strings of symbols. Pacific J. Math. 85, 261–294 (1979)
Cassaigne, J.: Motifs évitables et régularité dans les mots, Ph.D. thesis, Université Paris VI (1994)
Clark, R.J.: Avoidable formulas in combinatorics on words, Ph.D. thesis, University of California, Los Angeles (2001)
Currie, J.D., Lafrance, P.: Avoidability index for binary patterns with reversal. Electron. J. Combin. 23(1) (2016). Paper #P1.36
Currie, J., Mol, L., Rampersad, N.: A family of formulas with reversal of high avoidability index (Submitted)
Currie, J., Mol, L., Rampersad, N.: On avoidability of formulas with reversal (Submitted)
Currie, J., Rampersad, N.: Binary words avoiding \(xx^Rx\) and strongly unimodal sequences. J. Integer Seq. 15, Article 15.10.3 (2015)
Currie, J., Rampersad, N.: Growth rate of binary words avoiding \(xxx^R\). Theoret. Comput. Sci. 609, 456–468 (2016)
Du, C.F., Mousavi, H., Rowland, E., Schaeffer, L., Shallit, J.: Decision algorithms for Fibonacci-automatic words, II: related sequences and avoidability. Theoret. Comput. Sci. 657, 146–162 (2017)
Gawrychowski, P., I, T., Inenaga, S., Köppl, D., Manea, F.: Efficiently finding all maximal alpha-gapped repeats. In: Proceedings of the STACS, pp. 39:1–39:14 (2016)
Gawrychowski, P., Manea, F., Nowotka, D.: Testing generalised freeness of words. In: Proceedings of the STACS, pp. 337–349 (2014)
Kosolobov, D., Manea, F., Nowotka, D.: Detecting unary patterns. ArXiv preprint: https://arxiv.org/abs/1604.00054
Zimin, A.I.: Blocking sets of terms. Math. USSR Sbornik 47(2), 353–364 (1984). (English translation)
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Rampersad, N. (2017). Formulas with Reversal. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_10
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DOI: https://doi.org/10.1007/978-3-319-58741-7_10
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