**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])

$$\frac{1}{2} \cdot 4^{n} + \frac{1}{n + 1}{2 \, n \choose n} - {2 \, n + 1 \choose n} + {2 \, n - 1 \choose n - 1}$$

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

[1]

[2]

**Jefferson, A. F.***The substitution decomposition of matchings and RNA secondary structures*MathSciNet:3439033[2]

**Saule, Cédric, Régnier, M., Steyaert, J.-M., Denise, A.***Counting RNA pseudoknotted structures*MathSciNet:2843853Created

Apr 18, 2017 at 16:13 by

**Manda Riehl**Updated

Apr 22, 2017 at 15:15 by

**Martin Rubey**searching the database

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