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dc.contributor.authorBiswas, Arindam
dc.contributor.authorSaha, Jyoti Prakash
dc.date.accessioned2019-07-09T12:41:00Z
dc.date.available2019-07-09T12:41:00Z
dc.date.issued2019-07-09
dc.identifier.urihttp://publications.mfo.de/handle/mfo/2509
dc.description.abstractA pair of non-empty subsets $(W,W')$ in an abelian group $G$ is a complement pair if $W+W'=G$. $W'$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \forall \,w'\in W'$. In general, given an arbitrary subset in a group, the existence of minimal complement(s) depends on its structure. The dual problem asks that given such a set, if it is a minimal complement to some subset. We study tightness property of complement pairs $(W,W')$ such that both $W$ and $W'$ are minimal to each other. These are termed co-minimal pairs and we show that any non-empty finite set in an arbitrary free abelian group belongs to some co-minimal pair. We also construct infinite sets forming co-minimal pairs. Finally, we remark that a result of Kwon on the existence of minimal self-complements in $\mathbb{Z}$, also holds in any abelian group.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relationAlso published in: Journal of Number Theory 223(2021), pp. 350–370. https://doi.org/10.1016/j.jnt.2020.10.010en_US
dc.relation.ispartofseriesOberwolfach Preprints;2019,19
dc.subjectAdditive complementsen_US
dc.subjectMinimal complementsen_US
dc.subjectSunsetsen_US
dc.subjectAdditive number theoryen_US
dc.titleOn Co-Minimal Pairs in Abelian Groupsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2019-19
local.scientificprogramOWLF 2019en_US
local.series.idOWP-2019-19en_US
local.subject.msc11en_US
local.subject.msc05en_US
dc.identifier.urnurn:nbn:de:101:1-2019082214494868153160
dc.identifier.ppn1672108039


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