Minimal additive complements in finitely generated abelian groups
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Minimal additive complements in finitely generated abelian groups. / Biswas, Arindam; Saha, Jyoti Prakash.
I: Ramanujan Journal, Bind 57, 2022, s. 215–238.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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