We show the image of rooted tree maps forms a subspace of the kernel of the evaluation map of multiple $L$-values. To prove this, we define the diamond product as a modified harmonic product and describe its properties. We also show that $\tau$-conjugate rooted tree maps are their antipodes.

中文翻译：

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从谐波代数的角度看多个 L 值的有根树图

我们展示了有根树图的图像，形成了多个 $L$ -value 的评估图的内核的子空间。为了证明这一点，我们将金刚石乘积定义为改性谐波乘积并描述其特性。我们还表明 $\tau$ -conjugate rooted tree map 是它们的对跖点。