Duality and tangles of set separations

Reinhard Diestel; Christian Elbracht; Joshua Erde; Maximilian Teegen

Duality and tangles of set separations

Reinhard Diestel, Christian Elbracht, Joshua Erde, Maximilian Teegen

Institute of Discrete Mathematics (5050)

Research output: Contribution to journal › Article › peer-review

Abstract

Applications of tangles of connectivity systems suggest a duality between these, in which for two sets $X$ and $Y\!$ the elements $x$ of $X$ map to subsets $Y_x$ of $Y\!$, and the elements $y$ of $Y\!$ map to subsets $X_y$ of $X$, so that $x\in X_y$ if and only if $y\in Y_x$ for all $x\in X$ and $y\in Y\!$. We explore this duality, and relate the tangles arising from the dual systems to each other.

Original language	English
Number of pages	43
Journal	Journal of Combinatorics
Publication status	Accepted/In press - 2022

Keywords

Tangles
Seperation Systems
Clustering

Access to Document

2109.08398v1Submitted manuscript, 646 KBLicence: CC BY 4.0

Cite this

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title = "Duality and tangles of set separations",

abstract = " Applications of tangles of connectivity systems suggest a duality between these, in which for two sets $X$ and $Y\!$ the elements $x$ of $X$ map to subsets $Y_x$ of $Y\!$, and the elements $y$ of $Y\!$ map to subsets $X_y$ of $X$, so that $x\in X_y$ if and only if $y\in Y_x$ for all $x\in X$ and $y\in Y\!$. We explore this duality, and relate the tangles arising from the dual systems to each other. ",

keywords = "Tangles, Seperation Systems, Clustering",

author = "Reinhard Diestel and Christian Elbracht and Joshua Erde and Maximilian Teegen",

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year = "2022",

language = "English",

journal = "Journal of Combinatorics",

issn = "2156-3527",

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T1 - Duality and tangles of set separations

AU - Diestel, Reinhard

AU - Elbracht, Christian

AU - Erde, Joshua

AU - Teegen, Maximilian

N1 - This is the extended version of this paper

PY - 2022

Y1 - 2022

N2 - Applications of tangles of connectivity systems suggest a duality between these, in which for two sets $X$ and $Y\!$ the elements $x$ of $X$ map to subsets $Y_x$ of $Y\!$, and the elements $y$ of $Y\!$ map to subsets $X_y$ of $X$, so that $x\in X_y$ if and only if $y\in Y_x$ for all $x\in X$ and $y\in Y\!$. We explore this duality, and relate the tangles arising from the dual systems to each other.

AB - Applications of tangles of connectivity systems suggest a duality between these, in which for two sets $X$ and $Y\!$ the elements $x$ of $X$ map to subsets $Y_x$ of $Y\!$, and the elements $y$ of $Y\!$ map to subsets $X_y$ of $X$, so that $x\in X_y$ if and only if $y\in Y_x$ for all $x\in X$ and $y\in Y\!$. We explore this duality, and relate the tangles arising from the dual systems to each other.

KW - Tangles

KW - Seperation Systems

KW - Clustering

M3 - Article

SN - 2156-3527

JO - Journal of Combinatorics

JF - Journal of Combinatorics

ER -