A Note on the Equidistribution of 3-Colour Partitions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Males, Joshua
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212122
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Note on the Equidistribution of 3-Colour Partitions. Joshua Males. SIGMA 20 (2024), 001, 8 pages

In this short note, we prove equidistribution results regarding three families of three-colour partitions recently introduced by Schlosser and Zhou. To do so, we prove an asymptotic formula for the infinite product ₐ,c(ζ; e⁻ᶻ) := ∏ₙ≥₀ (1 − ζe⁻⁽ᵃ⁺ᶜⁿ⁾ᶻ) (, c ∈ ℕ with 0 < ≤ c and ζ a root of u...