Geodesic
Playing Nim on a simplicial complex
The electronic journal of combinatorics, Tome 3 (1996) no. 1
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We introduce a generalization of the classical game of Nim by placing the piles on the vertices of a simplicial complex and allowing a move to affect the piles on any set of vertices that forms a face of the complex. Under certain conditions on the complex we present a winning strategy. These conditions are satisfied, for instance, when the simplicial complex consists of the independent sets of a binary matroid. Moreover, we study four operations on a simplicial complex under which games on the complex behave nicely. We also consider particular complexes that correspond to natural generalizations of classical Nim.
DOI : 10.37236/1233
Classification : 91A05, 91A46
Mots-clés : Nim, generalization, winning strategy, simplicial complex 
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     author = {Richard Ehrenborg and Einar Steingr{\'\i}msson},
     title = {Playing {Nim} on a simplicial complex},
     journal = {The electronic journal of combinatorics},
     year = {1996},
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     number = {1},
     doi = {10.37236/1233},
     zbl = {0852.90132},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1233/}
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Richard Ehrenborg; Einar Steingrímsson. Playing Nim on a simplicial complex. The electronic journal of combinatorics, Tome 3 (1996) no. 1. doi: 10.37236/1233

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