MathDB

Let

n

be positive integer and fix

2n

distinct points on a circle. Determine the number of ways to connect the points with

n

arrows (oriented line segments) such that all of the following conditions hold: [*]each of the

2n

points is a startpoint or endpoint of an arrow; [*]no two arrows intersect; and [*]there are no two arrows

\overrightarrow{AB}

and

\overrightarrow{CD}

such that

A

B

C

and

D

appear in clockwise order around the circle (not necessarily consecutively).

Problem Statement