Skip to main content
SpringerLink
Log in

Lattices of Games

  • Published:
Order Aims and scope Submit manuscript

Abstract

We show that, for any set S of combinatorial games, the set of games all of whose immediate options belong to S forms a complete lattice. If every option of a game in S also lies in S, then this lattice is completely distributive.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Albert, M., Nowakowski, R.J., Wolfe, D.: Lessons in Play. A.K. Peters, Wellesley (2007)

    MATH  Google Scholar 

  2. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for your Mathematical Plays, 2nd edn., vols. 1–4. A.K. Peters, Wellesley (2001–2004)

  3. Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1967)

  4. Calistrate, D., Paulhus, M., Wolfe, D.: On the lattice structure of finite games. In: Nowakowski, R. (ed.) More Games of No Chance, pp. 25–30. Cambridge University Press, Mathematical Sciences Research Institute Publications 42 (2002)

  5. Conway, J.H.: On Numbers and Games, 2nd edn. A.K. Peters, Wellesley (2001)

    MATH  Google Scholar 

  6. Fraser, W., Hirshberg, S., Wolfe, D.: The structure of the distributive lattice of games born by day n. Integers 5(2), A6, 11 pp. (2005, electronic)

  7. Raney, G.N.: Completely distributive complete lattices. Proc. Am. Math. Soc. 3(5), 677–680 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  8. Siegel, A.N.: Combinatorial Game Suite. http://cgsuite.sourceforge.net/ (2000)

  9. Tunnicliffe, W.R.: On defining “completely distributive”. Algebra Univers. 19(3), 397–398 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  10. Wolfe, D., Fraser, W.: Counting the number of games. Theor. Comput. Sci. 313, 527–532 (2004)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Otago, Dunedin, New Zealand

    Michael Henry Albert

  2. Department of Mathematics & Statistics, Dalhousie University, Halifax, NS B3J 3H5, Canada

    Richard J. Nowakowski

Authors
  1. Michael Henry Albert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Richard J. Nowakowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Henry Albert.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Albert, M.H., Nowakowski, R.J. Lattices of Games. Order 29, 75–84 (2012). https://doi.org/10.1007/s11083-011-9198-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-011-9198-0

Keywords

Search

Navigation