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Communication Dans Un Congrès Année : 2021

Disorders and Permutations

Résumé

The additive x-disorder of a permutation is the sum of the absolute differences of all pairs of consecutive elements. We show that the additive x-disorder of a permutation of S(n), n ≥ 2, ranges from n − 1 to n 2 /2 − 1, and we give a complete characterization of permutations having extreme such values. Moreover, for any positive integers n and d such that n ≥ 2 and n − 1 ≤ d ≤ n 2 /2 − 1, we propose a linear-time algorithm to compute a permutation π ∈ S(n) with additive x-disorder d.
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Dates et versions

hal-03388489 , version 1 (20-10-2021)

Identifiants

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Laurent Bulteau, Samuele Giraudo, Stéphane Vialette. Disorders and Permutations. 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021), Jul 2021, Wroclaw, Poland. ⟨10.4230/LIPIcs.CPM.2021.11⟩. ⟨hal-03388489⟩
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