Combinatorics of Balanced set-valued labellings on pseudomanifolds

• Main Authors: Tu ,Jean Jay, 涂俊傑
• Other Authors: Lee,Shyh Nan
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/55350746900327533748

碩士 === 中原大學 === 應用數學研究所 === 83 === In this paper,we start with the combinatorial version of Stoke' s theorem which was proved in Kuhn's paper(1974). The main purpose of this thesis is to extend this theorem to set-valued labellings on pseudomanifolds, generalizing Shapley's theorem to pseudomanifolds as well. By this way, we get a new combinatorial formula on pseudomanifolds. To this end, we review some definitions concerning pseudomani- folds and combinatorial properties of π-balanced, π- subbalanced sets. In the proof of our main theorem, the basic ideas come from the Ky-Fan's "additive properties", and the methodo;ogy of this paper consists of matrix (det- erminant) computations, convex geometry, some topological results, and so on. Reduce to the singleton-valued case, our theorem of the set-valued labellings would cover the oriented Sperner's lemma (1961) and Ky-Fan's lemma (1984) as well.