{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:21:35Z","timestamp":1758824495506,"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>An occurrence of a consecutive permutation pattern $p$ in a permutation $\\pi$ is a segment of consecutive letters of $\\pi$ whose values appear in the same order of size as the letters in $p$.  The set of all permutations forms a poset with respect to such pattern containment.  We compute the M\u00f6bius function of intervals in this poset.  For most intervals our results give an immediate answer to the question.  In the remaining cases, we give a polynomial time algorithm to compute the M\u00f6bius function.  In particular, we show that the M\u00f6bius function only takes the values $-1$, $0$ and  $1$.<\/jats:p>","DOI":"10.37236\/633","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:44:01Z","timestamp":1578714241000},"source":"Crossref","is-referenced-by-count":7,"title":["The M\u00f6bius Function of the Consecutive Pattern Poset"],"prefix":"10.37236","volume":"18","author":[{"given":"Antonio","family":"Bernini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luca","family":"Ferrari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Einar","family":"Steingr\u00edmsson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,7,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p146\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p146\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:08:05Z","timestamp":1579302485000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p146"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/633","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,7,15]]},"article-number":"P146"}}