Permutations that separate close elements, and rectangle packings in the torus

2023/06/06 by Simon R. Blackburn⋆, Tuvi Etzion, Blackburn, Simon R. +1
Engineering · Mathematics · #05A05 #05B40 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2306.03685

openalex publication_date 2023/06/06 · openalex created_date 2023/06/09 · openalex updated_date 2026/07/28

Abstract

Let n, s and k be positive integers. For distinct i,j∈ℤ_n, define ||i,j||_n to be the distance between i and j when the elements of ℤ_n are written in a circle. So ||i,j||_n=min\(i-j)\bmod n,(j-i)\bmod n\. A permutation π:ℤ_n→\mathbb Z_n is (s,k)-clash-free if ||π(i),π(j)||_n≥ k whenever ||i,j||_n

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