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arXiv · 1206.0966

Permutations all of whose patterns of a given length are distinct

Peter Hegarty
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Abstract

For each integer k >= 2, let F(k) denote the largest n for which there exists a permutation σ\in S_n, all of whose patterns of length k are distinct. We prove that F(k) = k + \lfloor \sqrt{2k-3} \rfloor + e_k, where e_k \in {-1,0} for every k. Suggestions for further investigations along these lines are discussed.

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Peter Hegarty. 2012-06-10. Permutations all of whose patterns of a given length are distinct. https://arxiv.org/abs/1206.0966

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