论文标题
关于由二进制扩展双层混合关系定义的正式多个Zeta空间的计算
Computations about formal multiple zeta spaces defined by binary extended double shuffle relations
论文作者
论文摘要
我们使用计算机考虑的正式多个Zeta空间是$ \ Mathbb {f} _2 $ - 向量空间，由$ 2^{k-2} $生成的给定权重$ K $的正式符号，其中该符号满足二进制扩展的双层洗牌关系。最多重量$ k = 22 $，我们计算形式的多个Zeta空间的尺寸，并验证实际多个Zeta值的原始扩展双层式关系的尺寸构想。我们的计算采用高斯向前消除，并提供通过深度过滤的空间的信息。我们可以观察到，深度逐步的正式多个Zeta空间的尺寸具有霍夫曼多指数期望的pascal三角形模式。
The formal multiple zeta space we consider with a computer is an $\mathbb{F}_2$-vector space generated by $2^{k-2}$ formal symbols for a given weight $k$, where the symbols satisfy binary extended double shuffle relations. Up to weight $k=22$, we compute the dimensions of the formal multiple zeta spaces, and verify the dimension conjecture on original extended double shuffle relations of real multiple zeta values. Our computations adopt Gaussian forward elimination and give information for spaces filtered by depth. We can observe that the dimensions of the depth-graded formal multiple zeta spaces have a Pascal triangle pattern expected by the Hoffman mult-indices.
