A Note on the Equidistribution of 3-Colour Partitions
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2024 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212122 |
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| 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862559550104666112 |
|---|---|
| author | Males, Joshua |
| author_facet | Males, Joshua |
| citation_txt | A Note on the Equidistribution of 3-Colour Partitions. Joshua Males. SIGMA 20 (2024), 001, 8 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 unity) when lies in certain sectors in the right half-plane, which may be useful in studying similar problems. As a corollary, we obtain the asymptotic behaviour of the three-colour partition families at hand.
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| first_indexed | 2026-03-13T07:50:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212122 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T07:50:29Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Males, Joshua 2026-01-28T14:01:14Z 2024 A Note on the Equidistribution of 3-Colour Partitions. Joshua Males. SIGMA 20 (2024), 001, 8 pages 1815-0659 2020 Mathematics Subject Classification: 11P82 arXiv:2307.12955 https://nasplib.isofts.kiev.ua/handle/123456789/212122 https://doi.org/10.3842/SIGMA.2024.001 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 unity) when lies in certain sectors in the right half-plane, which may be useful in studying similar problems. As a corollary, we obtain the asymptotic behaviour of the three-colour partition families at hand. The author thanks W. Craig, M. Schlosser, and N.H. Zhou and the referees for many helpful comments on this note, in particular, for pointing out the related paper of Liu and Zhou [7]. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Note on the Equidistribution of 3-Colour Partitions Article published earlier |
| spellingShingle | A Note on the Equidistribution of 3-Colour Partitions Males, Joshua |
| title | A Note on the Equidistribution of 3-Colour Partitions |
| title_full | A Note on the Equidistribution of 3-Colour Partitions |
| title_fullStr | A Note on the Equidistribution of 3-Colour Partitions |
| title_full_unstemmed | A Note on the Equidistribution of 3-Colour Partitions |
| title_short | A Note on the Equidistribution of 3-Colour Partitions |
| title_sort | note on the equidistribution of 3-colour partitions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212122 |
| work_keys_str_mv | AT malesjoshua anoteontheequidistributionof3colourpartitions AT malesjoshua noteontheequidistributionof3colourpartitions |