A Study of Sperner's Lemma on Squares

• Main Authors: CHI-WEN CHOU, 周啓文
• Other Authors: Shyh-nan Lee
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/60737111947191652442

碩士 === 中原大學 === 應用數學研究所 === 103 === The purpose of this thesis is to study a generalization result of oriented Sperner's lemma for a triangulation of a square. In 2002 , Loera , Peterson and Su proved a generalized Sperner's lemma for a triangulation of a polytope . In this thesis , we give a proof of oriented Loera - Peterson - Su. Theorem when a polytope is a square. We apply Fan's door - to - door principle (an expression of path - following argument) to a Sperner's labeling of a triangulation of a square with two initial edges other than one.