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Characterising bimodal collections of sets in finite groups

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Characterising bimodal collections of sets in finite groups. / Huczynska, Sophie; Paterson, Maura.

In: Archiv der Mathematik, Vol. First Online, 09.07.2019.

Research output: Contribution to journalArticlepeer-review

Harvard

Huczynska, S & Paterson, M 2019, 'Characterising bimodal collections of sets in finite groups', Archiv der Mathematik, vol. First Online. https://doi.org/10.1007/s00013-019-01361-2

APA

Huczynska, S., & Paterson, M. (2019). Characterising bimodal collections of sets in finite groups. Archiv der Mathematik, First Online. https://doi.org/10.1007/s00013-019-01361-2

Vancouver

Huczynska S, Paterson M. Characterising bimodal collections of sets in finite groups. Archiv der Mathematik. 2019 Jul 9;First Online. https://doi.org/10.1007/s00013-019-01361-2

Author

Huczynska, Sophie ; Paterson, Maura. / Characterising bimodal collections of sets in finite groups. In: Archiv der Mathematik. 2019 ; Vol. First Online.

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@article{fc219681874344e7a6ce2e780d7d433b,
title = "Characterising bimodal collections of sets in finite groups",
abstract = "A collection of disjoint subsets A = {A1, A2, ..., Am} of a finite abelian group has the bimodal property if each non-zero group element δ either never occurs as a difference between an element of Ai and an element of Aj with j ≠ i, or else for every element ai in Ai there is an element aj ∈ Aj for some j ≠ i with ai - aj = δ. This property arises in familiar situations, such as cosets of a fixed subgroup or in a group partition, and has applications to the construction of optimal algebraic manipulation detection codes. In this paper, we obtain a structural characterisation for bimodal collections of sets.",
keywords = "Finite groups, Disjoint subsets, External differences",
author = "Sophie Huczynska and Maura Paterson",
year = "2019",
month = jul,
day = "9",
doi = "10.1007/s00013-019-01361-2",
language = "English",
volume = "First Online",
journal = "Archiv der Mathematik",
issn = "0003-889X",
publisher = "Birkhauser Verlag Basel",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Characterising bimodal collections of sets in finite groups

AU - Huczynska, Sophie

AU - Paterson, Maura

PY - 2019/7/9

Y1 - 2019/7/9

N2 - A collection of disjoint subsets A = {A1, A2, ..., Am} of a finite abelian group has the bimodal property if each non-zero group element δ either never occurs as a difference between an element of Ai and an element of Aj with j ≠ i, or else for every element ai in Ai there is an element aj ∈ Aj for some j ≠ i with ai - aj = δ. This property arises in familiar situations, such as cosets of a fixed subgroup or in a group partition, and has applications to the construction of optimal algebraic manipulation detection codes. In this paper, we obtain a structural characterisation for bimodal collections of sets.

AB - A collection of disjoint subsets A = {A1, A2, ..., Am} of a finite abelian group has the bimodal property if each non-zero group element δ either never occurs as a difference between an element of Ai and an element of Aj with j ≠ i, or else for every element ai in Ai there is an element aj ∈ Aj for some j ≠ i with ai - aj = δ. This property arises in familiar situations, such as cosets of a fixed subgroup or in a group partition, and has applications to the construction of optimal algebraic manipulation detection codes. In this paper, we obtain a structural characterisation for bimodal collections of sets.

KW - Finite groups

KW - Disjoint subsets

KW - External differences

U2 - 10.1007/s00013-019-01361-2

DO - 10.1007/s00013-019-01361-2

M3 - Article

VL - First Online

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

ER -

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