| Summary: | 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.
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