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Winning Strategies for Generalized Zeckendorf Game
Steven J. Miller, Eliel Sosis, Jingkai Ye
Zeckendorf proved that every positive integer can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence…
Winning Strategy for the Multiplayer and Multialliance Zeckendorf Games
Anna Cusenza, Aidan Dunkelberg, Kate Huffman +7
Edouard Zeckendorf proved that every positive integer can be uniquely written \cite{Ze} as the sum of non-adjacent Fibonacci numbers, known as the Zeckendorf decomposition. Bas…
Extending Zeckendorf's Theorem to a Non-constant Recurrence and the Zeckendorf Game on this Non-constant Recurrence Relation
Elżbieta Bołdyriew, Anna Cusenza, Linglong Dai +16
Zeckendorf's Theorem states that every positive integer can be uniquely represented as a sum of non-adjacent Fibonacci numbers, indexed from . This has been gene…
Bounds on Zeckendorf Games
Anna Cusenza, Aiden Dunkelberg, Kate Huffman +7
Zeckendorf proved that every positive integer can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this decomposition to construct a two-player game. Gi…