Annals of Combinatorics 2 (1998) 197-210

Heap Games, Numeration Systems and Sequences

Aviezri S. Fraenkel

Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel,

Received June 3, 1998

AMS Subject Classification: 90D46, 05A99

Abstract. We propose and analyze 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 it 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.

Keywords: heap games, numeration systems, sequences


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