标题： Arrow 定理与 Sperner 引理之间的联系 显示英文标题

标题： The connection between Arrow theorem and Sperner lemma

摘要： 众所周知，Sperner引理与Brouwer不动点定理是等价的。Tanaka [12]证明了Brouwer定理与Arrow定理是等价的，因此Arrow定理与Sperner引理是等价的。在本文中，我们将直接证明这个结果。此外，我们描述了许多其他与Arrow定理等价的陈述。 显示英文摘要

摘要： It is well known that Sperner lemma is equivalent to Brouwer fixed-point theorem. Tanaka [12] proved that Brouwer theorem is equivalent to Arrow theorem, hence Arrow theorem is equivalent to Sperner lemma. In this paper we will prove this result directly. Moreover, we describe a number of other statements equivalent to Arrow theorem.