An Observation on 7-distance Set in Euclidean Plane

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/88394

Title:	An Observation on 7-distance Set in Euclidean Plane
Authors:	瓦宇力;Budianto, Wahyu Tri
Contributors:	數學系
Keywords:	平面7-距離集;直徑圖;凸多邊形;planar 7-distance set;diameter graph;convex polygon
Date:	2022-06-16
Issue Date:	2022-07-14 01:11:50 (UTC+8)
Publisher:	國立中央大學
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。 ;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 \|.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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