歐式空間二距離集合之探討;A study of two-distance set in Euclidean space

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/85084

Title:	歐式空間二距離集合之探討;A study of two-distance set in Euclidean space
Authors:	林軒宇;Lin, Xuan-Yu
Contributors:	數學系
Keywords:	二距離集合;球面二距離集合;Two-distance set;Spherical two-distance set
Date:	2020-10-20
Issue Date:	2021-03-18 17:37:20 (UTC+8)
Publisher:	國立中央大學
Abstract:	在此論文中，首先先介紹二距離集合的定義，以及相關的文獻探討。之後介紹二個計算最大二距離集合個數的方法，線性規劃和半正定規劃。以及列出在 3 和 4 維中，若固定兩個內積值，去找此集合上界為整數的構造，與計算這些構造的最小能量是否為現在找出來的最小的解。然後用線性規劃證明當內積值為 ?1、0，最大二距離集合的上限為 2n。最後列出 3 維中，特殊角的構造和 3 維二距離集合個數為 5 個點和 6 個點的所有構造。 ;In this thesis, we first introduce the definition of the two-distance set and the related literature discussion. Second, two methods for calculating the maximum two-distance set are introduced, graph representation, linear programming and semidefinite programming method. Third, we try to find the structures if the upper bound of such two-distance set are integer, and check whether it is an energy minimization configuration. Fourth, when the inner product values are ?1 and 0, using linear programming to prove that, the maximum two-distance set is 2n. Finally, the constructions of two-distance set of the special angles and the cardinality of two-distance set with 5 points and 6 points are listed in 3-dimensions.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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