Meandric Systems

number of points n

4

random α

α = 3,2,1,4

random β

β = 1,4,3,2

This Demonstration shows a graphical representation of a meandric system. A meandric system is a set of closed planar curves that intersect a horizontal line

2n

times. A meander is a meandric system with one connected component. Meandric systems are in bijection with pairs of noncrossing set partitions [1]. The meandric system is shown in red, while the

α

(upper) and

β

(lower) noncrossing set partitions are shown in black; singletons are not displayed. Select the number of points

n

with the top slider. Then click the

α

and

β

buttons to generate a new plot.