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# Journal of Combinatorics

## Volume 15 (2024)

### Number 1

### Duality and tangles of set separations

Pages: 1 – 39

DOI: https://dx.doi.org/10.4310/JOC.2024.v15.n1.a1

#### Authors

#### 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, homology

#### 2010 Mathematics Subject Classification

05C83

Received 20 September 2021

Accepted 7 July 2022

Published 7 November 2023