Geodesic
Efficient counting and asymptotics of \(k\)-noncrossing tangled diagrams
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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 $c_k>0$.
DOI : 10.37236/126
Classification : 05C30, 05C10, 05C78
Mots-clés : noncrossing tangled diagrams, labeled graph, horizontal line, arcs, crossings, nestings, asymptotic formula 
@article{10_37236_126,
     author = {William Y. C. Chen and Jing Qin and Christian M. Reidys and Doron Zeilberger},
     title = {Efficient counting and asymptotics of \(k\)-noncrossing tangled diagrams},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/126},
     zbl = {1159.05027},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/126/}
}
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William Y. C. Chen; Jing Qin; Christian M. Reidys; Doron Zeilberger. Efficient counting and asymptotics of \(k\)-noncrossing tangled diagrams. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/126

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