Handshakes across a (round) table. (English) Zbl 1228.05031
Summary: We establish an explicit formula for the number of chord diagrams on \(2n\) points with \(k\) short chords and compute the expected number of short chords in a chord diagram.
MSC:
| 05A15 | Exact enumeration problems, generating functions |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
| 05A19 | Combinatorial identities, bijective combinatorics |
Software:
OEISOnline Encyclopedia of Integer Sequences:
Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.
Triangle of Dyck paths counted by number of long interior inclines.
