Arrays, numeration systems and Frankenstein games

We de ne an in nite array A of nonnegative integers based on a linear recurrence, whose second row provides basis elements of an exotic ternary numeration system. Using the numeration system we explore many properties of A. Further, we propose and analyze a family Frankenstein of 2-player pebbling games played on a semi-in nite strip, and present a winning strategy based on certain subarrays of A. Though the strategy looks easy, it is actually computationally hard. The numeration system is then used to decide whether the family has an e cient strategy or not.

• Type: Journal
• Year: 2002
• Where: TCS
• Authors: Aviezri S. Fraenkel
• Keywords: Exotic Ternary Numeration, Nite Array, Nonnegative Integers, TCS 2002, Theoretical Computer Science