The maximal length of a k-separator permutation
Name
Gunby-2014-The maximal length.pdf
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290.13 KB
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Checksum (MD5)
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Author(s)
Gunby, Benjamin P.
Date Issued
August 2014
Journal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Gunby, Benjamin. "The maximal length of a k-separator permutation." The Electronic Journal of Combinatorics Volume 21, Issue 3 (2014).
Version
Final published version
Abstract
A permutation σ ∈ S[subscript n] is a k-separator if all of its patterns of length k are distinct. Let F(k) denote the maximal length of a k-separator. Hegarty (2013) showed that k + ⌊√2k − 1⌋ − 1 ≤ F(k) ≤ k + ⌊√2k − 3⌋, and conjectured that F(k) = k + ⌊√2k − 1⌋ − 1. This paper will strengthen the upper bound to prove the conjecture for all sufficiently large k (in particular, for all k ≥ 320801).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.37236/3765
