Minimal additive complements in finitely generated abelian groups

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Minimal additive complements in finitely generated abelian groups. / Biswas, Arindam; Saha, Jyoti Prakash.

In: Ramanujan Journal, Vol. 57, 2022, p. 215–238.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Biswas, A & Saha, JP 2022, 'Minimal additive complements in finitely generated abelian groups', Ramanujan Journal, vol. 57, pp. 215–238. https://doi.org/10.1007/s11139-021-00421-y

APA

Biswas, A., & Saha, J. P. (2022). Minimal additive complements in finitely generated abelian groups. Ramanujan Journal, 57, 215–238. https://doi.org/10.1007/s11139-021-00421-y

Vancouver

Biswas A, Saha JP. Minimal additive complements in finitely generated abelian groups. Ramanujan Journal. 2022;57:215–238. https://doi.org/10.1007/s11139-021-00421-y

Author

Biswas, Arindam ; Saha, Jyoti Prakash. / Minimal additive complements in finitely generated abelian groups. In: Ramanujan Journal. 2022 ; Vol. 57. pp. 215–238.

Bibtex

@article{7f887c21dd4346b4b82e3b24acb8ac73,
title = "Minimal additive complements in finitely generated abelian groups",
abstract = "Given two nonempty subsets W, W′⊆ G in an arbitrary abelian group G, the set W′ is said to be an additive complement to W if W+ W′= G and it is minimal if no proper subset of W′ is a complement to W. The notion was introduced by Nathanson and previous works by him, Chen–Yang, Kiss–S{\'a}ndor–Yang, etc. focussed on G= Z. In this article, we focus on the higher rank case. We introduce the notion of “spiked subsets” and give necessary and sufficient conditions for the existence of minimal complements for them. This provides an answer to a problem of Nathanson in several contexts.",
keywords = "Additive complements, Additive number theory, Minimal complements, Sumsets",
author = "Arindam Biswas and Saha, {Jyoti Prakash}",
year = "2022",
doi = "10.1007/s11139-021-00421-y",
language = "English",
volume = "57",
pages = "215–238",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Minimal additive complements in finitely generated abelian groups

AU - Biswas, Arindam

AU - Saha, Jyoti Prakash

PY - 2022

Y1 - 2022

N2 - Given two nonempty subsets W, W′⊆ G in an arbitrary abelian group G, the set W′ is said to be an additive complement to W if W+ W′= G and it is minimal if no proper subset of W′ is a complement to W. The notion was introduced by Nathanson and previous works by him, Chen–Yang, Kiss–Sándor–Yang, etc. focussed on G= Z. In this article, we focus on the higher rank case. We introduce the notion of “spiked subsets” and give necessary and sufficient conditions for the existence of minimal complements for them. This provides an answer to a problem of Nathanson in several contexts.

AB - Given two nonempty subsets W, W′⊆ G in an arbitrary abelian group G, the set W′ is said to be an additive complement to W if W+ W′= G and it is minimal if no proper subset of W′ is a complement to W. The notion was introduced by Nathanson and previous works by him, Chen–Yang, Kiss–Sándor–Yang, etc. focussed on G= Z. In this article, we focus on the higher rank case. We introduce the notion of “spiked subsets” and give necessary and sufficient conditions for the existence of minimal complements for them. This provides an answer to a problem of Nathanson in several contexts.

KW - Additive complements

KW - Additive number theory

KW - Minimal complements

KW - Sumsets

UR - http://www.scopus.com/inward/record.url?scp=85104327851&partnerID=8YFLogxK

U2 - 10.1007/s11139-021-00421-y

DO - 10.1007/s11139-021-00421-y

M3 - Journal article

AN - SCOPUS:85104327851

VL - 57

SP - 215

EP - 238

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

ER -

ID: 261617072