@article{99b3f699ac8743b1849f0aec0bd3acc7,
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}",
note = "Funding Information: We wish to thank the anonymous reviewer. The first author acknowledges the fellowship of the Erwin Schr{\"o}dinger International Institute for Mathematics and Physics (ESI) and would also like to thank the Fakult{\"a}t f{\"u}r Mathematik, Universit{\"a}t Wien where a part of the work was carried out. Funding Information: Jyoti Prakash would like to acknowledge the Initiation Grant from the Indian Institute of Science Education and Research Bhopal, and the INSPIRE Faculty Award IFA18-MA123 from the Department of Science and Technology, Government of India. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2022",
month = jan,
day = "1",
doi = "10.1007/s11139-021-00421-y",
language = "English",
volume = "57",
pages = "215--238",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer Netherlands",
number = "1",
}