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Abstract for Richard Ehrenborg and Einar Steingr\'{\i}msson, Playing Nim on a Simplicial Complex

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.

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