Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

More Restricted Growth Functions: Gray Codes and Exhaustive Generation

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

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)

    Article  MathSciNet  MATH  Google Scholar 

  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

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vincent Vajnovszki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincent Vajnovszki.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

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

Keywords

Search

Navigation