{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:33:27Z","timestamp":1762522407111,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 ${n \\choose k}$ 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 $M_k(p)$ with an underlying set $M_k'(p)$. We study the question of when we can reconstruct $p$ from its multiset or its set of minors. We prove there exists an $N_k$ for every $k$ such that any permutation with length at least $N_k$ is reconstructible from its multiset of $(n-k)$-minors. We find the bounds $N_k &gt; k+\\log_2 k$ and $N_k  &lt;  {k^2\\over4} + 2k + 4$. For the number $N_k'$, giving the minimal length for permutations to be reconstructible from their sets of $(n-k)$-minors, we have the bound $N_k' &gt; 2k$. We work towards analogous bounds in the case when we restrict ourselves to layered permutations.<\/jats:p>","DOI":"10.37236\/1092","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:59:15Z","timestamp":1578718755000},"source":"Crossref","is-referenced-by-count":4,"title":["Permutation Reconstruction from Minors"],"prefix":"10.37236","volume":"13","author":[{"given":"Mariana","family":"Raykova","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,8,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r66\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r66\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:10:04Z","timestamp":1579320604000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r66"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1092","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,8,3]]},"article-number":"R66"}}