Zachary Louis Vasseur

collaborators

4 papers

math.CO2025

Linear Recurrences from Counting Schreier-Type Multisets

Hung Viet Chu, Yubo Geng, Julian King +3

A nonempty set $F$ is Schreier if $min F \geq ∣ F ∣$ . Bird observed that counting Schreier sets in a certain way produces the Fibonacci sequence. Since then, various connections betwe…

math.CO2025

Linear Recurrences of Generalized Schreier Sets Revisited

Hung Viet Chu, Zachary Louis Vasseur

For $p, q \in N$ , a finite nonempty set $F$ is said to be $(p, q)$ -Schreier (or maximal $(p, q)$ -Schreier, respectively) if $q min F \geq p ∣ F ∣$ (or $q min F = p ∣ F ∣$ , respective…

math.GM2024

Fixed-Term Decompositions Using Even-Indexed Fibonacci Numbers

Hung Viet Chu, Aney Manish Kanji, Zachary Louis Vasseur

As a variant of Zeckendorf's theorem, Chung and Graham proved that every positive integer can be uniquely decomposed into a sum of even-indexed Fibonacci numbers, whose coefficient…

math.CO2024

Weighted Schreier-type Sets and the Fibonacci Sequence

Hung Viet Chu, Zachary Louis Vasseur

For a finite set $A \subset N$ and $k \in N$ , let $ω_{k} (A) = \sum_{i \in A, i \neq = k} 1$ . For each $n \in N$ , define $$a_{k, n}\ =\ |\{E\subset \mathbb{N}\,:\, E…