{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:35Z","timestamp":1753893815625,"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>In this paper, we enumerate $k$-noncrossing tangled diagrams. A tangled diagram is a labeled graph with vertices $1,\\dots,n$, having degree at most two, which are arranged in increasing order in a horizontal line. The arcs are drawn in the upper halfplane with a particular notion of crossings and nestings. Our main result is the asymptotic formula for the number of $k$-noncrossing tangled diagrams $T_{k}(n) \\, \\sim \\,c_k \\, n^{-((k-1)^2+(k-1)\/2)}\\, (4(k-1)^2+2(k-1)+1)^n$ for some $c_k&gt;0$.<\/jats:p>","DOI":"10.37236\/126","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:32:58Z","timestamp":1578717178000},"source":"Crossref","is-referenced-by-count":2,"title":["Efficient Counting and Asymptotics of $k$-Noncrossing Tangled Diagrams"],"prefix":"10.37236","volume":"16","author":[{"given":"William Y. C.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Jing","family":"Qin","sequence":"additional","affiliation":[]},{"given":"Christian M.","family":"Reidys","sequence":"additional","affiliation":[]},{"given":"Doron","family":"Zeilberger","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,3,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:05:28Z","timestamp":1579316728000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/126","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,3,13]]},"article-number":"R37"}}