Sperner' s Lemma and Matriods

• Main Authors: Ching-Liang Tseng, 曾慶良
• Other Authors: Shyh-Nan Lee
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/83059263023926490626

碩士 === 中原大學 === 數學系 === 87 === The purpose of this master's thesis is to give a comprehensive study of a recent result of Shih and Lee[1] in the field of combinatorics of simplexes. The celebrated Sperner's lemma[3] which is a purely combinatorial result can be used to prove the Brouwer fixed point theorem which is one of the most important tools in nonlinear analysis. Matroid version of Sperner's lemma combining the triangulatuion of a simplex with a matroid structure was first considered by Lovasz[2] but the main theorem in his article is wrong as it stands. We modify the conditions in the theorem and give a detail study of the so called Sperner matroid theory. In this thesis, we discuss the affine space in section 1, properties of simplexes are studied in section 2, some basic results concerned with triangulations of simplexes are proved in setion 3, and our main theorem is presented and proved in setion 4. Every statement in this thesis is discussed in detail as possible as we can, these details would be helpful for more advanced research.