1
vote
0answers
37 views

Triangulations of the concave polygon

It is known that the amount of possible triangulations of the convex polygon by disjoint diagonals is the Catalan number. But can we somehow know possible amount of the triangulations of the concave ...
1
vote
0answers
67 views

Corresponding Triangulations of an (n+2)-gon to n Segments Connecting n+1 Collinear Points

So I'm asked to count the number of ways of connecting n+1 collinear points with n line segments subjected to the following constraints: If the line is L 1) No segment passes below L. 2) Starting at ...
8
votes
2answers
166 views

Why does the term ${\frac{1}{n-1}} {2n-4\choose n-2}$ counts the number of possible triangulations in a polygon?

In the given picture bellow, it counts the number of different triangloations in a polygon, how do the get to this expression, why is it: $$ {2n-4\choose n-2} $$ and why do we multiply it by ...