Ren Watson

collaborators

4 papers

math.NT2026

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.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 $k \geq 3$ , every nonnegative integer has a unique $k$ -Zeckendorf representation as a sum of distinct $k$ -bonacci numbers, where no $k$ conse…

math.AG2025

Almost All Transverse-Free Plane Curves Are Trivially Transverse-Free

Alejandro Lopez, Bella Villarreal, Ren Watson +1

We call a curve $C \subset P^{2}$ defined over $F_{q}$ \textit{transverse-free} if for every line, $ℓ$ , over $F_{q}$ , $C \cap ℓ$ is not a smooth dimensio…