All Questions
4
questions
4
votes
1
answer
896
views
Recursivley count triangulations of a convex polygon
I am trying to find a recursive number of different triangulations of a convex polygon with $n$ vertices.
After some searching I found that the number can be expressed using catalan numbers, this ...
1
vote
0
answers
190
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 ...
- 11
1
vote
1
answer
195
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 ...
- 4,093
9
votes
2
answers
432
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 $${\...
- 1,661