Embedding processes in combinatorial game theory

  • Authors:

  • Carlos Pereira dos Santos

  • Affiliations:

  • -

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

Berlekamp asked the question ''What is the habitat of *2?'' (See Guy, 1996 [6].) It is possible to generalize the question and ask ''For a game G, what is the largest n such that *n is a position of G?'' This leads to the concept of the nim dimension. In Santos and Silva (2008) [8] a fractal process was proposed for analyzing the previous questions. For the same purpose, in Santos and Silva (2008) [9], an algebraic process was proposed. In this paper we implement a third idea related to embedding processes. With Alan Parr's traffic lights, we exemplify the idea of estimating the ''difficulty'' of the game and proving that its nim dimension is infinite.