Heap games, numeration systems and sequences

Details Heap games, numeration systems and sequences Heap games, numeration systems and sequences

1998-09-14

arxiv.org/abs/math/9809074v1

Mathematics

Combinatorics

To appear in Annals of Combinatorics

Scientific paper

We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used, which enables us to decide whether the family has an efficient strategy or not. We introduce yet another class of sequences, and demonstrate its equivalence with the class of sequences defined for the strategy of our games.

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