ON ADDITIVE REPRESENTATION FUNCTIONS Article Swipe
YA-LI LI
,
Yong-Gao Chen
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1017/s0004972717000302
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.1017/s0004972717000302
For any finite abelian group $G$ with $|G|=m$ , $A\subseteq G$ and $g\in G$ , let $R_{A}(g)$ be the number of solutions of the equation $g=a+b$ , $a,b\in A$ . Recently, Sándor and Yang [‘A lower bound of Ruzsa’s number related to the Erdős–Turán conjecture’, Preprint, 2016, arXiv:1612.08722v1 ] proved that, if $m\geq 36$ and $R_{A}(n)\geq 1$ for all $n\in \mathbb{Z}_{m}$ , then there exists $n\in \mathbb{Z}_{m}$ such that $R_{A}(n)\geq 6$ . In this paper, for any finite abelian group $G$ with $|G|=m$ and $A\subseteq G$ , we prove that (a) if the number of $g\in G$ with $R_{A}(g)=0$ does not exceed $\frac{7}{32}m-\frac{1}{2}\sqrt{10m}-1$ , then there exists $g\in G$ such that $R_{A}(g)\geq 6$ ; (b) if $1\leq R_{A}(g)\leq 6$ for all $g\in G$ , then the number of $g\in G$ with $R_{A}(g)=6$ is more than $\frac{7}{32}m-\frac{1}{2}\sqrt{10m}-1$ .
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- article
- Language
- en
- Landing Page
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- https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6789C7E8157020E146D5211974F7E8DC/S0004972717000302a.pdf/div-class-title-on-additive-representation-functions-div.pdf
- OA Status
- diamond
- Cited By
- 1
- References
- 15
- Related Works
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- OpenAlex ID
- https://openalex.org/W2964200455
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https://openalex.org/W2964200455Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1017/s0004972717000302Digital Object Identifier
- Title
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ON ADDITIVE REPRESENTATION FUNCTIONSWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2017Year of publication
- Publication date
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2017-05-02Full 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/10.1017/s0004972717000302Publisher landing page
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https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6789C7E8157020E146D5211974F7E8DC/S0004972717000302a.pdf/div-class-title-on-additive-representation-functions-div.pdfDirect link to full text PDF
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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://www.cambridge.org/core/services/aop-cambridge-core/content/view/6789C7E8157020E146D5211974F7E8DC/S0004972717000302a.pdf/div-class-title-on-additive-representation-functions-div.pdfDirect OA link when available
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Abelian group, Mathematics, Combinatorics, ConjectureTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2018: 1Per-year citation counts (last 5 years)
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15Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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