{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:46Z","timestamp":1753893826919,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a given permutation $\\tau$, let $P_N^{\\tau}$ be the uniform probability distribution on the set of $N$-element permutations $\\sigma$ that avoid the pattern $\\tau$. For $\\tau=\\mu_k:=123\\ldots k$, we consider $P_N^{\\mu_k}(\\sigma_I=J)$ where $I\\sim\u00a0\\gamma N$ and $J\\sim\u00a0\\delta N$ for $\\gamma, \\delta \\in (0,1)$. If $\\gamma+ \\delta \\neq 1$, then we are in the large deviations regime with the probability decaying exponentially, and we calculate the limiting value of $P_N^{\\mu_k}(\\sigma_I=J)^{1\/N}$. We also observe that for $\\tau = \\lambda_{k,\\ell} := 12\\ldots\\ell k(k-1)\\ldots(\\ell+1)$ and $\\gamma+\\delta&lt;1$, the limit of $P_N^{\\tau}(\\sigma_I=J)^{1\/N}$ is the same\u00a0 as for $\\tau=\\mu_k$.<\/jats:p>","DOI":"10.37236\/6225","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:45:16Z","timestamp":1578685516000},"source":"Crossref","is-referenced-by-count":4,"title":["Large Deviations for Permutations Avoiding Monotone Patterns"],"prefix":"10.37236","volume":"23","author":[{"given":"Neal","family":"Madras","sequence":"first","affiliation":[]},{"given":"Lerna","family":"Pehlivan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,12,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:06:59Z","timestamp":1579237619000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,9]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6225","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,12,9]]},"article-number":"P4.36"}}