Geodesic
Winning positions in simplicial Nim
The electronic journal of combinatorics, Tome 17 (2010)
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Simplicial Nim, introduced by Ehrenborg and Steingrímsson, is a generalization of the classical two-player game of Nim. The heaps are placed on the vertices of a simplicial complex and a player's move may affect any number of piles provided that the corresponding vertices form a face of the complex. In this paper, we present properties of a complex that are equivalent to the $\cal P$-positions (winning positions for the second player) being closed under addition. We provide examples of such complexes and answer a number of open questions posed by Ehrenborg and Steingrímsson.
DOI : 10.37236/356
Classification : 91A05, 91A43, 91A44, 91A46
Mots-clés : simplicial Nim, \(\mathcal P\)-positions, simplicial complex, graph complex 
@article{10_37236_356,
     author = {David Horrocks},
     title = {Winning positions in simplicial {Nim}},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/356},
     zbl = {1188.91014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/356/}
}
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David Horrocks. Winning positions in simplicial Nim. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/356

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