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Generating Cyclic 2-Gray Codes for Fibonacci q-Decreasing Words

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WALCOM: Algorithms and Computation (WALCOM 2024)

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Abstract

We present a two-stage algorithm for generating cyclic 2-Gray codes for q-decreasing words. In the first step, a simple recursive algorithm is used to generate a cyclic 2-Gray code for q-run constrained words, which are q-decreasing words that start with a 0. Then, by considering the first block of 1 s and concatenating cyclic Gray code listings of q-run constrained words of different length n, we construct the first known cyclic 2-Gray code for q-decreasing words for all positive real numbers q.

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Acknowledgements

This research is supported by the Macao Polytechnic University research grant (Project code: RP/FCA-02/2022). The research of the first author is also supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (MSIT), Korea (No. 2020R1F1A1A01070666).

A part of this work was done while the first author was visiting Kanazawa University in Japan. The first author would like to thank Hiroshi Fujisaki for his hospitality during his stay in Kanazawa.

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Authors and Affiliations

  1. Faculty of Applied Sciences, Macao Polytechnic University, Macao, China

    Dennis Wong, Bowie Liu, Chan-Tong Lam & Marcus Im

  2. Department of Computer Science, State University of New York, Incheon, Korea

    Dennis Wong

Authors
  1. Dennis Wong
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  2. Bowie Liu
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  3. Chan-Tong Lam
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  4. Marcus Im
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Corresponding author

Correspondence to Dennis Wong .

Editor information

Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Ryuhei Uehara

  2. Iwate University, Morioka, Japan

    Katsuhisa Yamanaka

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

Appendix: Python code to generate q-decreasing words and q-run constrained words in cyclic 2-Gray code order

Appendix: Python code to generate q-decreasing words and q-run constrained words in cyclic 2-Gray code order

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Wong, D., Liu, B., Lam, CT., Im, M. (2024). Generating Cyclic 2-Gray Codes for Fibonacci q-Decreasing Words. In: Uehara, R., Yamanaka, K., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2024. Lecture Notes in Computer Science, vol 14549. Springer, Singapore. https://doi.org/10.1007/978-981-97-0566-5_8

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  • DOI: https://doi.org/10.1007/978-981-97-0566-5_8

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-97-0565-8

  • Online ISBN: 978-981-97-0566-5

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