Permutation Reconstruction from Minors

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Permutation Reconstruction from Minors
We consider the problem of permutation reconstruction, which is a variant of graph reconstruction. Given a permutation p of length n, we delete k of its entries in each possible way to obtain n k subsequences. We renumber the sequences from 1 to n-k preserving the relative size of the elements to form (n-k)-minors. These minors form a multiset Mk(p) with an underlying set Mk(p). We study the question of when we can reconstruct p from its multiset or its set of minors. We prove there exists an Nk for every k such that any permutation with length at least Nk is reconstructible from its multiset of (n-k)-minors. We find the bounds Nk > k+log2 k and Nk < k2 4 +2k+4. For the number Nk, giving the minimal length for permutations to be reconstructible from their sets of (n - k)-minors, we have the bound Nk > 2k. We work towards analogous bounds in the case when we restrict ourselves to layered permutations.
Mariana Raykova
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Authors Mariana Raykova
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