Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao International Journa...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
International Journal of Game Theory
Article . 1992 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1992
Data sources: zbMATH Open
versions View all 2 versions
addClaim

This Research product is the result of merged Research products in OpenAIRE.

You have already added 0 works in your ORCID record related to the merged Research product.

Mathematical kayles

Mathematical Kayles
Authors: Sibert, W. L.; Conway, J. H.;

Mathematical kayles

Abstract

Kayles, first introduced by \textit{H. E. Dudeney} [``Canterbury puzzles'' (London 1910), p. 118, p. 120] and \textit{S. Loyd} [``Cyclopedia of tricks and puzzles'' (New York 1914), p. 232], is an impartial combinatorial game, played with rows of skittles. Two players alternatively remove a single skittle or two contiguous ones. The winner in normal play is the person who removes the last skittle. In misère play this person is the loser. Kayles was one of first nontrivial games to be analyzed [the reviewer and \textit{C. A. B. Smith}, Proc. Cambridge Philos. Soc. 52, 514--526 (1956; Zbl 0074.34503)],using the Sprague-Grundy theory [\textit{R. P. Sprague}, Tôhoku Math. J. 41, 438--444 (1936; Zbl 0013.29004); \textit{P. M. Grundy}, Eureka 2, 6--8 (1939)], which doesn't apply to misère play, whose analysis is much more recalcitrant [\textit{P. M. Grundy} and \textit{C. A. B. Smith}, Proc. Cambridge Philos. Soc. 52, 527--533 (1956; Zbl 0074.34504); the second author, ``On numbers and games'' (1976; Zbl 0334.00004)]. Now Kayles reappears as the first nontrivial game to reveal its misère analysis. Since then \textit{T. Plambeck} [Theor. Comput. Sci. 96, No. 2, 361--388 (1992; Zbl 0777.90095)] has used the Sibert- Conway type of analysis to settle the game of Daisies (Guy-Smith code 4.7) and other games having a similar (normal play) nim-sequence.

Related Organizations
Keywords

Kayles, misère analysis, impartial combinatorial game, Combinatorial games, nim-like games

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    7
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Average
Top 10%
Average
Upload OA version
Are you the author of this publication? Upload your Open Access version to Zenodo!
It’s fast and easy, just two clicks!