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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國立政治大學
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| Online Access: | http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22B2002002892%22. |
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ndltd-CHENGCHI-B20020028922013-01-07T19:23:00Z 凸多邊形的三角化與二元樹的一對一證明 A Bijective Proof from Triangulated Convex Polygons to Binary Trees 李世仁 Lee, Shih-Jen 凸多邊的三角形化 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)). 國立政治大學 http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22B2002002892%22. text 英文 Copyright © nccu library on behalf of the copyright holders |
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NDLTD |
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英文 |
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NDLTD |
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凸多邊的三角形化 |
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凸多邊的三角形化 李世仁 Lee, Shih-Jen 凸多邊形的三角化與二元樹的一對一證明 |
| description |
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)). |
| author |
李世仁 Lee, Shih-Jen |
| author_facet |
李世仁 Lee, Shih-Jen |
| author_sort |
李世仁 |
| title |
凸多邊形的三角化與二元樹的一對一證明 |
| title_short |
凸多邊形的三角化與二元樹的一對一證明 |
| title_full |
凸多邊形的三角化與二元樹的一對一證明 |
| title_fullStr |
凸多邊形的三角化與二元樹的一對一證明 |
| title_full_unstemmed |
凸多邊形的三角化與二元樹的一對一證明 |
| title_sort |
凸多邊形的三角化與二元樹的一對一證明 |
| publisher |
國立政治大學 |
| url |
http://thesis.lib.nccu.edu.tw/cgi-bin/cdrfb3/gsweb.cgi?o=dstdcdr&i=sid=%22B2002002892%22. |
| work_keys_str_mv |
AT lǐshìrén tūduōbiānxíngdesānjiǎohuàyǔèryuánshùdeyīduìyīzhèngmíng AT leeshihjen tūduōbiānxíngdesānjiǎohuàyǔèryuánshùdeyīduìyīzhèngmíng AT lǐshìrén abijectiveprooffromtriangulatedconvexpolygonstobinarytrees AT leeshihjen abijectiveprooffromtriangulatedconvexpolygonstobinarytrees |
| _version_ |
1716458488100552704 |