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The lengths for which bicrucial square-free permutations exist

Authors :
Groenland, Carla
Johnston, Tom
Publication Year :
2021

Abstract

A square is a factor $S = (S_1; S_2)$ where $S_1$ and $S_2$ have the same pattern, and a permutation is said to be square-free if it contains no non-trivial squares. The permutation is further said to be bicrucial if every extension to the left or right contains a square. We completely classify for which $n$ there exists a bicrucial square-free permutation of length $n$.<br />Comment: 24 pages, 4 figures

Subjects

Subjects :
Mathematics - Combinatorics

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2109.00502
Document Type :
Working Paper
Full Text :
https://doi.org/10.54550/ECA2022V2S4PP4