Abstract
A sumber is a sum of ups, downs and star. Sumbers can describe the positions of many partisan infinitesimal games. Earlier, we provided a simplification rule [6] that can determine whether a game G is a sumber or not, and if it is, determine the exact sumber of G from its left and right options, G L and G R. This article extends the previous result and presents three variations of colored heap games; each of them can be solved by sumbers.
This paper is sponsored by National Science Council, Taiwan. [93-2213-E-346-006].
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References
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways. Academic Press, New York (1982)
Bouton, C.L.: Nim: A Game With a Complete Mathematical Theory. Annals of Mathematics 3, 35–39 (1902)
Conway, J.H.: On Numbers and Games. Academic Press, New York (1976)
Grundy, P.M.: Mathematics and Games. Eureka 2, 6–8 (1939); Reprinted in Eureka 27, 9–11 (1964)
Kao, K.Y.: On Hot and Tepid Combinatorial Games, PhD Thesis, University of North Carolina, Charlotte (1997)
Kao, K.Y.: Sumbers - Sums of Ups and Downs. Elec. Journal of Combinatorial Number Theory 5, G1 (2005)
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Kao, KY. (2006). On Colored Heap Games of Sumbers. In: van den Herik, H.J., Hsu, SC., Hsu, Ts., Donkers, H.H.L.M.(. (eds) Advances in Computer Games. ACG 2005. Lecture Notes in Computer Science, vol 4250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11922155_18
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DOI: https://doi.org/10.1007/11922155_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-48887-3
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