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Show that the number of triangulations of a regular n-gon is the same as the number...

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Advance Math

Show that the number of triangulations of a regular n-gon is thesame as the number of Catalan paths from (0,0) to (n?2, n?2).

A Catalan path is defined as the following:

we want to count the number of distinct paths from the point(0,0) to the point (n, n) subject to the following rules:

•We must stay inside the box [0, n]×[0, n].

•We move one step at a time, either moving one unit East or oneunit North.

•We cannot visit the same point twice.

•The path must always stay at or below the line y = x.

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