On the $r$-th Root Partition Function Article Swipe
Ya-Li Li
,
Yong-Gao Chen
·
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.11650/tjm.20.2016.6812
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.11650/tjm.20.2016.6812
The well known partition function $p(n)$ has a long research history, where $p(n)$\ndenotes the number of solutions of the equation $n = a_1 + \\cdots + a_k$ with\nintegers $1 \\leq a_1 \\leq \\cdots \\leq a_k$. In this paper, we investigate a new\npartition function. For any real number $r \\gt 1$, let $p_r(n)$ be the number of\nsolutions of the equation $n = \\lfloor \\sqrt[r]{a_1} \\rfloor + \\cdots + \\lfloor\n\\sqrt[r]{a_k} \\rfloor$ with integers $1 \\leq a_1 \\leq \\cdots \\leq a_k$, where\n$\\lfloor x \\rfloor$ denotes the greatest integer not exceeding $x$. In this paper, it\nis proved that $\\exp(c_1 n^{r/(r+1)}) \\leq p_r(n) \\leq \\exp(c_2n^{r/(r+1)})$ for two\npositive constants $c_1$ and $c_2$ (depending only $r$).
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Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.11650/tjm.20.2016.6812
- OA Status
- diamond
- Cited By
- 9
- References
- 2
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- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W2413415226Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.11650/tjm.20.2016.6812Digital Object Identifier
- Title
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On the $r$-th Root Partition FunctionWork title
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2016Year of publication
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2016-05-01Full publication date if available
- Authors
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Ya-Li Li, Yong-Gao ChenList of authors in order
- Landing page
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https://doi.org/10.11650/tjm.20.2016.6812Publisher landing page
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YesWhether a free full text is available
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diamondOpen access status per OpenAlex
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https://doi.org/10.11650/tjm.20.2016.6812Direct OA link when available
- Concepts
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Mathematics, Combinatorics, Partition (number theory), Integer (computer science), Function (biology), Partition function (quantum field theory), Physics, Biology, Programming language, Computer science, Quantum mechanics, Evolutionary biologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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9Total citation count in OpenAlex
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2024: 1, 2023: 3, 2022: 1, 2021: 2, 2018: 1Per-year citation counts (last 5 years)
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2Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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