Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions

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Standard

Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions. / Biswas, Arindam; Saha, Jyoti Prakash.

I: Ramanujan Journal, Bind 57, 2022, s. 1445–1462.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Biswas, A & Saha, JP 2022, 'Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions', Ramanujan Journal, bind 57, s. 1445–1462. https://doi.org/10.1007/s11139-021-00442-7

APA

Biswas, A., & Saha, J. P. (2022). Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions. Ramanujan Journal, 57, 1445–1462. https://doi.org/10.1007/s11139-021-00442-7

Vancouver

Biswas A, Saha JP. Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions. Ramanujan Journal. 2022;57:1445–1462. https://doi.org/10.1007/s11139-021-00442-7

Author

Biswas, Arindam ; Saha, Jyoti Prakash. / Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions. I: Ramanujan Journal. 2022 ; Bind 57. s. 1445–1462.

Bibtex

@article{48b5f47fb3e84d8a868ce53a4ce1f891,
title = "Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions",
abstract = "In 2011, Nathanson proposed several questions on minimal complements in a group or a semigroup. The notion of minimal complements and being a minimal complement leads to the notion of co-minimal pairs which was considered in a prior work of the authors. In this article, we study which type of subsets in the integers and free abelian groups of higher rank can be a part of a co-minimal pair. We show that a majority of lacunary sequences have this property. From the conditions established, one can show that any infinite subset of any finitely generated abelian group has uncountably many subsets which is a part of a co-minimal pair. Further, the uncountable collection of sets can be chosen so that they satisfy certain algebraic properties.",
keywords = "Additive complements, Additive number theory, Minimal complements, Representation of integers, Sumsets",
author = "Arindam Biswas and Saha, {Jyoti Prakash}",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2022",
doi = "10.1007/s11139-021-00442-7",
language = "English",
volume = "57",
pages = "1445–1462",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions

AU - Biswas, Arindam

AU - Saha, Jyoti Prakash

N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - In 2011, Nathanson proposed several questions on minimal complements in a group or a semigroup. The notion of minimal complements and being a minimal complement leads to the notion of co-minimal pairs which was considered in a prior work of the authors. In this article, we study which type of subsets in the integers and free abelian groups of higher rank can be a part of a co-minimal pair. We show that a majority of lacunary sequences have this property. From the conditions established, one can show that any infinite subset of any finitely generated abelian group has uncountably many subsets which is a part of a co-minimal pair. Further, the uncountable collection of sets can be chosen so that they satisfy certain algebraic properties.

AB - In 2011, Nathanson proposed several questions on minimal complements in a group or a semigroup. The notion of minimal complements and being a minimal complement leads to the notion of co-minimal pairs which was considered in a prior work of the authors. In this article, we study which type of subsets in the integers and free abelian groups of higher rank can be a part of a co-minimal pair. We show that a majority of lacunary sequences have this property. From the conditions established, one can show that any infinite subset of any finitely generated abelian group has uncountably many subsets which is a part of a co-minimal pair. Further, the uncountable collection of sets can be chosen so that they satisfy certain algebraic properties.

KW - Additive complements

KW - Additive number theory

KW - Minimal complements

KW - Representation of integers

KW - Sumsets

UR - http://www.scopus.com/inward/record.url?scp=85107593617&partnerID=8YFLogxK

U2 - 10.1007/s11139-021-00442-7

DO - 10.1007/s11139-021-00442-7

M3 - Journal article

AN - SCOPUS:85107593617

VL - 57

SP - 1445

EP - 1462

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

ER -

ID: 276954455