2016 Fiscal Year Final Research Report
Comprehensive research on minimum energy structures by design theory
Project/Area Number 
26800082

Research Category 
GrantinAid for Young Scientists (B)

Allocation Type  Multiyear Fund 
Research Field 
Foundations of mathematics/Applied mathematics

Research Institution  Kyushu Institute of Technology 
Principal Investigator 
Tagami Makoto 九州工業大学, 大学院情報工学研究院, 准教授 (50380671)

Project Period (FY) 
20140401 – 20170331

Keywords  デザイン / エネルギー最小化構造 / 調和指数デザイン / ハミングスキーム 
Outline of Final Research Achievements 
From the viewpoint of design theory in algebraic combinatorics, we carried out a search for minimum energy structures. Under the assumption of having the fixed moment, we constructed a computer program to make a search for distributions of finite points in Euclidean space which minimizes the energy for many kinds of potential functions. Using the program, we observed a pattern for the minimum energy structures on the plane. We considered the finite version for spherical designs of harmonic index t in the space, which is called Hamming scheme and studied well in coding theory. In particular, we gave the constructions and the classifications for designs of harmonic index t in Hamming scheme.

Free Research Field 
代数的組合せ論
