Skip to main content

Formulas with Reversal

  • Conference paper
  • First Online:
Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baker, K., McNulty, G., Taylor, W.: Growth problems for avoidable words. Theoret. Comput. Sci. 69, 319–345 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bean, D.R., Ehrenfeucht, A., McNulty, G.F.: Avoidable patterns in strings of symbols. Pacific J. Math. 85, 261–294 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cassaigne, J.: Motifs évitables et régularité dans les mots, Ph.D. thesis, Université Paris VI (1994)

    Google Scholar 

  4. Clark, R.J.: Avoidable formulas in combinatorics on words, Ph.D. thesis, University of California, Los Angeles (2001)

    Google Scholar 

  5. Currie, J.D., Lafrance, P.: Avoidability index for binary patterns with reversal. Electron. J. Combin. 23(1) (2016). Paper #P1.36

    Google Scholar 

  6. Currie, J., Mol, L., Rampersad, N.: A family of formulas with reversal of high avoidability index (Submitted)

    Google Scholar 

  7. Currie, J., Mol, L., Rampersad, N.: On avoidability of formulas with reversal (Submitted)

    Google Scholar 

  8. Currie, J., Rampersad, N.: Binary words avoiding \(xx^Rx\) and strongly unimodal sequences. J. Integer Seq. 15, Article 15.10.3 (2015)

    Google Scholar 

  9. Currie, J., Rampersad, N.: Growth rate of binary words avoiding \(xxx^R\). Theoret. Comput. Sci. 609, 456–468 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. 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)

    Article  MathSciNet  MATH  Google Scholar 

  11. 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)

    Google Scholar 

  12. Gawrychowski, P., Manea, F., Nowotka, D.: Testing generalised freeness of words. In: Proceedings of the STACS, pp. 337–349 (2014)

    Google Scholar 

  13. Kosolobov, D., Manea, F., Nowotka, D.: Detecting unary patterns. ArXiv preprint: https://arxiv.org/abs/1604.00054

  14. Zimin, A.I.: Blocking sets of terms. Math. USSR Sbornik 47(2), 353–364 (1984). (English translation)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Narad Rampersad .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-58741-7_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics