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math.NT2026
The Ordered Zeckendorf Game
Ivan Bortnovskyi, Michael Lucas, Steven J. Miller +3
We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every posit…
math.NT2025
Properties of Multidimensional Vector Zeckendorf Representations
Ivan Bortnovskyi, June Duvivier, Pedro Espinosa +7
Zeckendorf's Theorem says that for all , every nonnegative integer has a unique -Zeckendorf representation as a sum of distinct -bonacci numbers, where no conse…