{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:18:18Z","timestamp":1759335498716,"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>Let $LA_{n}(\\tau)$ be the length of the longest alternating subsequence of a uniform random permutation $\\tau\\in\\left[ n\\right] $. Classical probabilistic arguments are used to rederive the asymptotic mean, variance and limiting law of $LA_{n}\\left( \\tau\\right) $. Our methodology is robust enough to tackle similar problems for finite alphabet random words or even Markovian sequences in which case our results are mainly original. A sketch of how some cases of pattern restricted permutations can also be tackled with probabilistic methods is finally presented.<\/jats:p>","DOI":"10.37236\/440","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:58:52Z","timestamp":1578715132000},"source":"Crossref","is-referenced-by-count":8,"title":["A Probabilistic Approach to the Asymptotics of the Length of the Longest Alternating Subsequence"],"prefix":"10.37236","volume":"17","author":[{"given":"Christian","family":"Houdr\u00e9","sequence":"first","affiliation":[]},{"given":"Ricardo","family":"Restrepo","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,12,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r168\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r168\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:21:22Z","timestamp":1579303282000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r168"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/440","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,12,10]]},"article-number":"R168"}}