Efficient counting and asymptotics of k-noncrossing tangled diagrams

W.Y.C. Chen, J. Qin, C.M. Reidys, D. Zeilberger

Research output: Contribution to journalJournal articleResearchpeer-review


In this paper, we enumeratek-noncrossing tangled-diagrams. A tangled-diagramis a labeled graph with vertices 1, . . . , n, having degree≤2, which are arrangedin increasing order in a horizontal line. The arcs are drawn in the upper half-plane with a particular notion of crossings and nestings. Our main result is theasymptotic formula for the number ofk-noncrossing tangled-diagramsTk(n)∼ckn−((k−1)2+(k−1)/2)(4(k−1)2+ 2(k−1) + 1)nfor someck>0.
Original languageEnglish
JournalThe Electronic Journal of Combinatorics
Publication statusPublished - 2009
Externally publishedYes


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