Skip to main content
SpringerLink
Log in

Counting the Number of Three-Player Partizan Cold Games

  • Conference paper
Computers and Games (CG 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4630))

Included in the following conference series:

Abstract

We give upper and lower bounds on S 3[n] equal to the number of three-player partizan cold games born by day n. In particular, we give an upper bound of \(O(S_2[n]^3)\) and a lower bound of Ω(S 2[n]) where S 2[n] is the number of surreal numbers born by day n.

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
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

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, San Diego (1982)

    MATH  Google Scholar 

  2. Cincotti, A.: Three-Player Partizan Games. Theoretical Computer Science 332, 367–389 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Conway, J.H.: On Numbers and Games. Academic Press, San Diego (1976)

    MATH  Google Scholar 

  4. Knuth, D.: Surreal Numbers. Addison-Wesley, London, UK (1974)

    MATH  Google Scholar 

  5. Li, S.Y.R.: N-Person Nim and N-Person Moore’s Games. Game Theory 7, 31–36 (1978)

    Article  MATH  Google Scholar 

  6. Loeb, D.E.: Stable Winning Coalitions. In: Nowakowski, R.J. (ed.) Games of No Chance, vol. 29, pp. 451–471. MSRI Publ. Cambridge University Press (1994)

    Google Scholar 

  7. Propp, J.: Three-player Impartial games. Theoretical Computer Science 233, 263–278 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Straffin Jr., P.D.: Three-Person Winner-Take-All Games with Mc-Carthy’s Revenge Rule. College Journal of Mathetmatics 16, 386–394 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  9. Wolfe, D., Fraser, W.: Counting the Number of Games. Theoretical Computer Science 313, 527–532 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Unit for Computers and Games, School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Alessandro Cincotti

Authors
  1. Alessandro Cincotti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

H. Jaap van den Herik Paolo Ciancarini H. H. L. M. (Jeroen) Donkers

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cincotti, A. (2007). Counting the Number of Three-Player Partizan Cold Games. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.(. (eds) Computers and Games. CG 2006. Lecture Notes in Computer Science, vol 4630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75538-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75538-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75537-1

  • Online ISBN: 978-3-540-75538-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation