着色问题中的同伦与超越扩张
Homotopies and transcendental extensions in colouring problems
AI总结：
本文通过代数无关坐标的几何实现与有向体积方法，证明了广义Y博弈不可绘制性等新结果，并重新证明了Sperner引理多重标记版本等已知结论。
摘要：
我们发展了顶点坐标在实代数数域上代数无关的几何实现技术，并将其与受McLennan和Tourky关于Sperner引理工作启发的有向体积方法相结合。这使我们能够证明新结果：广义Y博弈的不可绘制性质、两个单纯形乘积的三角剖分定理、多重标记的Ky Fan引理，并给出已知结果的新证明：Sperner引理的多重标记版本和广义Atanassov猜想。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
