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Permutations that Separate Close Elements, and Rectangle Packings in the Torus

Year: 2024

Type: article

Abstract: Let $n$, $s$ and $k$ be positive integers. For distinct $i,j\in\mathbb{Z}_n$, define $||i,j||_n$ to be the distance between $i$ and $j$ when the elements of $\mathbb{Z}_n$ are written in a circle. So\[||i,j||_n=\min\{(i-j)\bmod n,(j-i)\bmod n\}.\]A permutation $\pi:\mathbb{Z}_n\rightarrow\mathbb {Z}_n$ is $(s,k)$-clash-free if $||\pi(i),\pi(j)||_n\geq k$ whenever $||i,j||_n

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12711

Authors: Simon R. Blackburn, Tuvi Etzion

Institutions: Royal Holloway University of London, Technion – Israel Institute of Technology

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403924849

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