| dc.contributor.advisor | 李陽明 | zh_TW |
| dc.contributor.advisor | Li, Young-Ming | en_US |
| dc.contributor.author (Authors) | 李世仁 | zh_TW |
| dc.contributor.author (Authors) | Lee, Shih-Jen | en_US |
| dc.creator (作者) | 李世仁 | zh_TW |
| dc.creator (作者) | Lee, Shih-Jen | en_US |
| dc.date (日期) | 1996 | en_US |
| dc.date.accessioned | 28-Apr-2016 13:29:59 (UTC+8) | - |
| dc.date.available | 28-Apr-2016 13:29:59 (UTC+8) | - |
| dc.date.issued (上傳時間) | 28-Apr-2016 13:29:59 (UTC+8) | - |
| dc.identifier (Other Identifiers) | B2002002892 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/87367 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 82155003 | zh_TW |
| dc.description.abstract (摘要) | 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)). | en_US |
| dc.description.tableofcontents | 1 Introduction 1 2 Triangulation of Polygon 2 2.1Traversal of triangulation..........2 2.2Triangulating..........5 3 Binary Search Trees 7 3.1Preliminary..........7 3.2Mapping..........8 4 Bijection on Unlabeled Binary Tress 14 4.1Existence..........14 4.2Bijectin..........16 5 Conclusion 20 A Counting Binary Tress 21 B Note 23 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#B2002002892 | en_US |
| dc.subject (關鍵詞) | 凸多邊的三角形化 | zh_TW |
| dc.title (題名) | 凸多邊形的三角化與二元樹的一對一證明 | zh_TW |
| dc.title (題名) | A Bijective Proof from Triangulated Convex Polygons to Binary Trees | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] Ralph P. Grimaldi. Discrete and Combinatorial Mathematics: A n Applied Introduction.3rd ed .Addison- Wesley, 1994. [2] Ellis Horowit.z and Sartaj Sahni . Fundamentals of Data Struchlres. Computer Science Press,Inc., 1982. [3] Richard A. Brualdi. Introductory Combinatorics. Elsevier North-Holland; Inc., 1977. [4] Jean-Paul Tremblay and Richard B. Bunt. An Introduction to Computer Science: An Algorithmic Approach.McGraw-Hill: Inc. , 1979. [5] C. L. Liu . Introduction to Combinatorial 111athcmatics. McGraw-Hill; Inc., 1968. | zh_TW |
