| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 瓦宇力 | zh_TW |
| DC.creator | Wahyu Tri Budianto | en_US |
| dc.date.accessioned | 2022-6-16T07:39:07Z | |
| dc.date.available | 2022-6-16T07:39:07Z | |
| dc.date.issued | 2022 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=108221602 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 在離散幾何中有個有趣的問題是尋找最大k-距離集。 即使看似簡單的最大平面7-距離集也還是未知的。
此篇論文我們給出部分結論。 Erdös and Fishburn [1] 給出了16個點的平面7距離集， 但不知道是否是最大的。 我們將17個點的平面7-距離集以X_D的基數做分類， 這個數會介於2到17之間。 我們照著 Wei [2] 的思路研究17個點的平面7-距離集。
我們證明9-13以外是不可能的， 但9-13的部分只能給出部分結論。 | zh_TW |
| dc.description.abstract | It is known that obtaining maximum k-distance sets has been an interesting problem in discrete geometry. Even a seemingly not-difficult problem like the maximum cardinality of 7-distance set in R^2 is yet to be found.
In this thesis we provide some partial results for this problem. Erdös and Fishburn [1] showed the 16-point 7-distance sets, but did not prove that 16 is the maximum. We observe whether there is any 17-point 7-distance set in R^2 based on the cardinality of X_D, where 2≤|X_D |≤17. We follow the method used in Wei [2] for this observation.
We can only provide partial results for 9≤|X_D |≤13, but for the other parts, we prove that there is no 17-point 7-distance set with that value of |X_D |. | en_US |
| DC.subject | 平面7-距離集 | zh_TW |
| DC.subject | 直徑圖 | zh_TW |
| DC.subject | 凸多邊形 | zh_TW |
| DC.subject | planar 7-distance set | en_US |
| DC.subject | diameter graph | en_US |
| DC.subject | convex polygon | en_US |
| DC.title | An Observation on 7-distance Set in Euclidean Plane | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |