The Maximal Length of a k-Separator Permutation
نویسنده
چکیده
A permutation σ ∈ Sn 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 6 F (k) 6 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).
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 21 شماره
صفحات -
تاریخ انتشار 2014