Identifier
Identifier
Values
[(1,6),(2,4),(3,5)] => 0
[(1,2),(3,6),(4,5)] => 1
[(1,4),(2,3),(5,6)] => 1
[(1,5),(2,3),(4,6)] => 1
[(1,4),(2,5),(3,6)] => 0
[(1,5),(2,6),(3,4)] => 1
[(1,3),(2,4),(5,6)] => 1
[(1,3),(2,5),(4,6)] => 0
[(1,3),(2,6),(4,5)] => 1
[(1,4),(2,6),(3,5)] => 1
[(1,6),(2,3),(4,5)] => 1
[(1,6),(2,5),(3,4)] => 1
[(1,2),(3,5),(4,6)] => 1
[(1,5),(2,4),(3,6)] => 1
[(1,2),(3,4),(5,6)] => 1
Description
The indicator function of whether a given perfect matching is an L & P matching.
An L&P matching is built inductively as follows:
starting with either a single edge, or a hairpin $([1,3],[2,4])$, insert a noncrossing matching or inflate an edge by a ladder, that is, a number of nested edges.
The number of L&P matchings is (see [thm. 1, 2])
$$\frac{1}{2} \cdot 4^{n} + \frac{1}{n + 1}{2 \, n \choose n} - {2 \, n + 1 \choose n} + {2 \, n - 1 \choose n - 1}$$
References
 Jefferson, A. F. The substitution decomposition of matchings and RNA secondary structures MathSciNet:3439033
 Saule, Cédric, Régnier, M., Steyaert, J.-M., Denise, A. Counting RNA pseudoknotted structures MathSciNet:2843853
Created
Apr 18, 2017 at 16:13 by Manda Riehl
Updated
Apr 22, 2017 at 15:15 by Martin Rubey