dc.contributor.author Biswas, Arindam dc.contributor.author Saha, Jyoti Prakash dc.date.accessioned 2019-07-09T12:41:00Z dc.date.available 2019-07-09T12:41:00Z dc.date.issued 2019-07-09 dc.identifier.uri http://publications.mfo.de/handle/mfo/2509 dc.description.abstract A 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.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation Also published in: Journal of Number Theory 223(2021), pp. 350–370. https://doi.org/10.1016/j.jnt.2020.10.010 en_US dc.relation.ispartofseries Oberwolfach Preprints;2019,19 dc.subject Additive complements en_US dc.subject Minimal complements en_US dc.subject Sunsets en_US dc.subject Additive number theory en_US dc.title On Co-Minimal Pairs in Abelian Groups en_US dc.type Preprint en_US dc.rights.license Dieses 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.license This 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.doi 10.14760/OWP-2019-19 local.scientificprogram OWLF 2019 en_US local.series.id OWP-2019-19 en_US local.subject.msc 11 en_US local.subject.msc 05 en_US dc.identifier.urn urn:nbn:de:101:1-2019082214494868153160 dc.identifier.ppn 1672108039
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