遞增樹中的交錯與嵌套
| dc.contributor | 游森棚 | zh_TW |
| dc.contributor | Eu, Sen-Peng | en_US |
| dc.contributor.author | 劉冠宏 | zh_TW |
| dc.contributor.author | Liu, Guan-Hong | en_US |
| dc.date.accessioned | 2025-12-09T08:11:43Z | |
| dc.date.available | 2025-08-13 | |
| dc.date.issued | 2025 | |
| dc.description.abstract | 這篇論文以遞增樹為研究對象, 探討其結構中的交錯與嵌套的性質和分布情形.首先, 定義在本篇論文中的遞增樹, 並舉例說明如何將Sn中的排列與遞增樹一一對應. 接著, 在遞增樹上看交錯與嵌套. 發現在特定的交錯數與嵌套數之下, 所對應的遞增樹有幾棵.更進一步發現按照交錯數與嵌套數來分類遞增樹會有對稱分布, 並給出相關生成函數的架構.最後, 考慮k-交錯與k-嵌套, 以及其弱版本, 並指出在遞增樹中這些性質的極大值之間亦具有某種對稱關係. | zh_TW |
| dc.description.abstract | none | en_US |
| dc.description.sponsorship | 數學系 | zh_TW |
| dc.identifier | 61140035S-48152 | |
| dc.identifier.uri | https://etds.lib.ntnu.edu.tw/thesis/detail/8acbcbd5c2d9119d628431cecf121ace/ | |
| dc.identifier.uri | http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/125511 | |
| dc.language | 中文 | |
| dc.subject | 遞增樹 | zh_TW |
| dc.subject | 交錯 | zh_TW |
| dc.subject | 嵌套 | zh_TW |
| dc.subject | 生成函數 | zh_TW |
| dc.subject | Increasing Tree | en_US |
| dc.subject | Crossing | en_US |
| dc.subject | Nesting | en_US |
| dc.subject | generating function | en_US |
| dc.title | 遞增樹中的交錯與嵌套 | zh_TW |
| dc.title | Crossing and Nesting in Increasing Tree | en_US |
| dc.type | 學術論文 |
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