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More Restricted Growth Functions: Gray Codes and Exhaustive Generation

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Abstract

A Gray code for a combinatorial class is a method for listing the objects in the class so that successive objects differ in some prespecified, small way, typically expressed as a bounded Hamming distance. In a previous work, the authors of the present paper showed, among other things, that the m-ary Reflected Gray Code Order yields a Gray code for the set of restricted growth functions. Here we further investigate variations of this order relation, and give the first Gray codes and efficient generating algorithms for bounded restricted growth functions.

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Notes

  1. In [4] a similar terminology is used for a slightly different notion

References

  1. Bernini, A., Bilotta, S., Pinzani, R., Sabri, A., Vajnovszki, V.: Reflected Gray codes for \(q\)-ary words avoiding a given factor. Acta. Inform. 52(7), 573–592 (2015)

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  2. Gray, F.: Pulse code communication, U.S. Patent 2632058 (1953)

  3. Ruskey, F.: Combinatorial generation, Book in preparation

  4. Sabri, A., Vajnovszki, V.: Reflected Gray code based orders on some restricted growth sequences. Comp. J. 58(5), 1099–1111 (2015)

    Article  Google Scholar 

  5. Sabri, A., Vajnovszki, V.: Bounded growth functions: Gray codes and exhaustive generation, The Japanese Conference on Combinatorics and its Applications, May 21–25, Kyoto, Japan (2016)

  6. Sloane, N.J.A.: The On-line Encyclopedia of Integer Sequences, available electronically at http://oeis.org

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Authors and Affiliations

  1. Center for Computational Mathematics Studies, Gunadarma University, Depok, Indonesia

    Ahmad Sabri

  2. LE2I, Université Bourgogne Franche-Comté, Dijon, France

    Vincent Vajnovszki

Authors
  1. Ahmad Sabri
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  2. Vincent Vajnovszki
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Correspondence to Vincent Vajnovszki.

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Sabri, A., Vajnovszki, V. More Restricted Growth Functions: Gray Codes and Exhaustive Generation. Graphs and Combinatorics 33, 573–582 (2017). https://doi.org/10.1007/s00373-017-1774-7

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  • DOI: https://doi.org/10.1007/s00373-017-1774-7

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