Skip to main content
SpringerLink
Log in

The Lattice Structure of Three-Player Games

  • Conference paper
Computers and Games (CG 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6515))

Included in the following conference series:

  • 1367 Accesses

Abstract

In combinatorial games, few results are known about the overall structure of three-player games. We prove that three-player games born by day d form a distributive lattice with respect to every partial order relation, but that the collection of all finite three-player games does not form a lattice.

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

Access this chapter

Log in via an institution
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 PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning ways for your mathematical plays. Academic Press, London (1982)

    MATH  Google Scholar 

  2. Calistrate, D., Paulhus, M., Wolfe, D.: On the lattice structure of finite games. In: Nowakowski, R.J. (ed.) More Games of No Chance, vol. 42, pp. 25–30. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  3. Cincotti, A.: Three-player partizan games. Theoretical Computer Science 332(1-3), 367–389 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Conway, J.H.: On numbers and games. Academic Press, London (1976)

    MATH  Google Scholar 

  5. Fraser, W., Hirshberg, S., Wolfe, D.: The structure of the distributive lattice of games born by day n. INTEGERS: Electronic Journal of Combinatorial Number Theory 5(2), #A06 (2005)

    MathSciNet  MATH  Google Scholar 

  6. Moews, D.: Sum of games born on days 2 and 3. Theoretical Computer Science 91(1), 119–128 (1991)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Alessandro Cincotti

Authors
  1. Alessandro Cincotti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Tilburg Center for Cognition and Communication (TiCC), Tilburg University, P.O. Box 90153, 5000LE, Tilburg, The Netherlands

    H. Jaap van den Herik  & Aske Plaat  & 

  2. Japan Advanced Institute of Science and Technology, Research Unit for Computers and Games, 1-1, Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Hiroyuki Iida

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cincotti, A. (2011). The Lattice Structure of Three-Player Games. In: van den Herik, H.J., Iida, H., Plaat, A. (eds) Computers and Games. CG 2010. Lecture Notes in Computer Science, vol 6515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17928-0_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17928-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17927-3

  • Online ISBN: 978-3-642-17928-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation