Modified Erdős-Ginzburg-Ziv Constants for $(\mathbb{Z}/n\mathbb{Z})^2$ Article Swipe
For an abelian group $G$ and an integer $t > 0$, the modified Erdős-Ginzburg-Ziv constant $s'_t(G)$ is the smallest integer $\ell$ such that any zero-sum sequence of length at least $\ell$ with elements in $G$ contains a zero-sum subsequence (not necessarily consecutive) of length $t$. We compute bounds for $s'_{t}(G)$ for $G = \left(\mathbb{Z}/n\mathbb{Z}\right)^2$ and $G = \left(\mathbb{Z}/n_1\mathbb{Z} \times \mathbb{Z}/n_2\mathbb{Z}\right)$. We also compute bounds for $G = \left(\mathbb{Z}/p\mathbb{Z}\right)^d$ where the subsequence can be any length in $\{p, \dots, (d-1)p\}$. Lastly, we investigate the Erdős-Ginzburg-Ziv constant for $G = \left(\mathbb{Z}/n\mathbb{Z}\right)^2$ and subsequences of length $tn$.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1907.11236
- https://arxiv.org/pdf/1907.11236
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4288279090
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Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4288279090Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.1907.11236Digital Object Identifier
- Title
-
Modified Erdős-Ginzburg-Ziv Constants for $(\mathbb{Z}/n\mathbb{Z})^2$Work title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-07-25Full publication date if available
- Authors
-
Trajan HammondsList of authors in order
- Landing page
-
https://arxiv.org/abs/1907.11236Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1907.11236Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1907.11236Direct OA link when available
- Concepts
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Subsequence, Combinatorics, Integer (computer science), Abelian group, Zero (linguistics), Constant (computer programming), Sequence (biology), Physics, Mathematics, Mathematical analysis, Computer science, Bounded function, Linguistics, Genetics, Philosophy, Biology, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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