论文标题
着色问题的同质和先验扩展
Homotopies and transcendental extensions in colouring problems
论文作者
论文摘要
我们开发了几何实现的技术，具有代数独立的（在真实代数数字的领域）的顶点坐标，并将其与麦克伦南和桑德尔在sperner章节上的作品启发的定向音量方法相结合。这使我们能够证明新的结果：广义Y游戏的非绘制属性，关于两个简单产品的三角剖分的定理，具有多列标记的Ky Fan的引理，并给出了已知结果的新证明：Sperner的多版本版本的sperner lemma的aymma和广义的Atanassovsupture。
We develop the technique of geometric realizations with algebraically independent (over the field of real algebraic numbers) coordinates of vertices and combine it with the oriented volume method inspired by work of McLennan and Tourky on the Sperner's lemma. This enables us to prove new results: the non-draw property of the generalized Y game, the theorem about triangulation of the product of two simplices, multilabeled Ky Fan' s lemma, and give new proofs of known results: the multilabeled version of Sperner's lemma and generalized Atanassov conjecture.
