A combinatorial proof of a fixed point property
A combinatorial proof of a fixed point property
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定点性质的组合证明
DOI：
10.1016/j.jcta.2012.01.004
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
K. Baclawski
中科院分区：
文献类型：
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作者：
K. Baclawski
发展了一类有限单纯复形，称为伪锥，它具有许多有用的组合性质。一个偏序集是伪锥，如果它的序复形是伪锥。伪锥可以通过多种方式由其他伪锥构造而成。伪锥序集包括有限可拆序集和有限截断非补格。本文的主要结果是给出了有限伪锥的固定单形性质的一个组合证明，其中构造了一个相互关联固定单形的组合结构。这给出了有限偏序集不动点理论中一些著名的非构造性结果的组合证明。
A class of finite simplicial complexes, called pseudo cones, is developed that has a number of useful combinatorial properties. A partially ordered set is a pseudo cone if its order complex is a pseudo cone. Pseudo cones can be constructed from other pseudo cones in a number of ways. Pseudo cone ordered sets include finite dismantlable ordered sets and finite truncated noncomplemented lattices. The main result of the paper is a combinatorial proof of the fixed simplex property for finite pseudo cones in which a combinatorial structure is constructed that relates fixed simplices to one another. This gives combinatorial proofs of some well known non-constructive results in the fixed point theory of finite partially ordered sets.