凸多邊形的三角化與二元樹的一對一證明
How many ways can a convex polygon of n（≥3） sides be triangulated by diagonals that do not intersect？ The problem was first proposed by Leonard Euler. Instead of setting up a recurrence relation and using the method of generating function to solve it, we shall set up a one-to-one correspondence betw...
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| Language: | 英文 |
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國立政治大學
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| Subjects: | |
| Online Access: | http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22B2002002892%22. |
| Summary: | How many ways can a convex polygon of n（≥3） sides be triangulated by diagonals that do not intersect？ The problem was first proposed by Leonard Euler. Instead of setting up a recurrence relation and using the method of generating function to solve it, we shall set up a one-to-one correspondence between the convex-polygon triangulations we are trying to count the rooted binary trees that have already been counted. Let bn denote the number of rooted ordered binary trees with n vertices and let tn denote the number of triangulations of convex polygon with n sides. We conclude that tn＝bn＝1/(n-1) ((2n-4)¦(n-2)). |
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