A Note on the Equidistribution of 3-Colour Partitions

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2024
• 1. Verfasser: Males, Joshua
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2024
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/212122
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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 𝐹ₐ,c(ζ; e⁻ᶻ) := ∏ₙ≥₀ (1 − ζe⁻⁽ᵃ⁺ᶜⁿ⁾ᶻ) (𝑎, c ∈ ℕ with 0 < 𝑎 ≤ c and ζ a root of un...