S. J. Miller

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20222025

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4 papers · 1 filter

math.NT2025

Comparing Left and Right Quotient Sets in Groups

Julian Duvivier, Xiaoyao Huang, Ava Kennon +5

For a finite subset $A$ of a group $G$ , we define the right quotient set and the left quotient set of $A$ , respectively, as $A A^{- 1} := {a_{1} a_{2}^{- 1} : a_{1}, a_{2} \in A}$ , $A^{-1}A := \…

math.NT2025

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.NT2024

Black Hole Zeckendorf Games

Caroline Cashman, Steven J. Miller, Jenna Shuffleton +1

Zeckendorf proved that every positive integer can be written as a decomposition of non-adjacent Fibonacci numbers. Baird-Smith, Epstein, Flint, and Miller converted the process of…

math.NT2022

Winning Strategies for Generalized Zeckendorf Game

Steven J. Miller, Eliel Sosis, Jingkai Ye

Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence…