Permutations that separate close elements

2022/07/20 by Simon R. Blackburn⋆, Blackburn, Simon R.
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #05A05 #05B45 #Combinatorics (math.CO) #FOS: Mathematics #Genome Rearrangement Algorithms #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2207.09806

openalex publication_date 2022/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

Let n be a fixed integer with n≥ 2. For 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 cycle. So ||i,j||_n=min\(i-j)\bmod n,(j-i)\bmod n\. For positive integers s and k, the permutation π:ℤ_n→ℤ_n is (s,k)-clash-free if ||π(i),π(j)||_n≥ k whenever ||i,j||_n

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