The maximal length of a k-separator permutation
Author(s)
Gunby, Benjamin P.
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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).
Date issued
2014-08Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
1077-8926