The Lengths for Which Bicrucial Square-Free Permutations Exist

Carla Groenland; Tom Johnston

doi:10.54550/eca2022v2s4pp4

The Lengths for Which Bicrucial Square-Free Permutations Exist

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

: A square is a factor S = (S1; S2) where S1 and S2 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.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Enumerative Combinatorics and Applications
Volume	2
Issue number	4
DOIs	https://doi.org/10.54550/eca2022v2s4pp4
Publication status	Published - 21 Jan 2022

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ECA2022_S4PP4Final published version, 737 KBLicence: CC BY-NC-ND

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abstract = ": A square is a factor S = (S1; S2) where S1 and S2 have the same pattern, and a permutation issaid to be square-free if it contains no non-trivial squares. The permutation is further said to be bicrucial ifevery extension to the left or right contains a square. We completely classify for which n there exists a bicrucialsquare-free permutation of length n.",

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N2 - : A square is a factor S = (S1; S2) where S1 and S2 have the same pattern, and a permutation issaid to be square-free if it contains no non-trivial squares. The permutation is further said to be bicrucial ifevery extension to the left or right contains a square. We completely classify for which n there exists a bicrucialsquare-free permutation of length n.

AB - : A square is a factor S = (S1; S2) where S1 and S2 have the same pattern, and a permutation issaid to be square-free if it contains no non-trivial squares. The permutation is further said to be bicrucial ifevery extension to the left or right contains a square. We completely classify for which n there exists a bicrucialsquare-free permutation of length n.

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M3 - Article

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JF - Enumerative Combinatorics and Applications

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The Lengths for Which Bicrucial Square-Free Permutations Exist

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