Clayton Mizgerd

most citedDeterministic Zeckendorf Games

4 citations · 10 across the 8 of their papers we have counts for

collaborators

8 papers

cs.DS2024

Rapid mixing of the down-up walk on matchings of a fixed size

Vishesh Jain, Clayton Mizgerd

Let $G = (V, E)$ be a graph on $n$ vertices and let $m^{*} (G)$ denote the size of a maximum matching in $G$ . We show that for any $δ > 0$ and for any $1 \leq k \leq (1 - δ) m^{*} (G)$ , the d…

math.CO2024

Inducibility of rainbow graphs

Emily Cairncross, Clayton Mizgerd, Dhruv Mubayi

Fix $k \geq 11$ and a rainbow $k$ -clique $R$ . We prove that the inducibility of $R$ is $k! / (k^{k} - k)$ . An extremal construction is a balanced recursive blow-up of $R$ . This answers a q…

math.NT2020★ 1 cited

Winning Strategy for the Multiplayer and Multialliance Zeckendorf Games

Anna Cusenza, Aidan Dunkelberg, Kate Huffman +7

Edouard Zeckendorf proved that every positive integer $n$ can be uniquely written \cite{Ze} as the sum of non-adjacent Fibonacci numbers, known as the Zeckendorf decomposition. Bas…

math.NT2020★ 2 cited

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 $1, 2, 3, 5, \dots$ . This has been gene…

math.NT2020

Bounds on Zeckendorf Games

Anna Cusenza, Aiden Dunkelberg, Kate Huffman +7

Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this decomposition to construct a two-player game. Gi…

math.NT2020★ 3 cited

Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, II

Thomas C. Martinez, Steven J. Miller, Clayton Mizgerd +2

Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers ${F_{n}}$ , where we take $F_{1} = 1$ and $F_{2} = 2$ …

math.NT2020★ 4 cited

Deterministic Zeckendorf Games

Ruoci Li, Xiaonan Li, Steven J. Miller +4

Zeckendorf proved that every positive integer can be written uniquely as the sum of non-adjacent Fibonacci numbers. We further explore a two-player Zeckendorf game introduced in Ba…

math.NT2020

Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, I

Thomas C. Martinez, Steven J. Miller, Clayton Mizgerd +1

Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers ${F_{n}}$ , where we take $F_{1} = 1$ and $F_{2} = 2$ …