Thakur [Tha10] showed that, for r, $s\in \mathbb{N}$, a product of two Carlitz zeta values ${\zeta }_A(r)$ and ${\zeta }_A(s)$ can be expressed as an ${\mathbb{F}}_p$-linear combination of ${\zeta }_A(r+s)$ and double zeta values of weight $r+s$. Such an expression is called shuffle relation by Thakur. Fixing r, $s\in \mathbb{N}$, we construct a t-module $E^{\prime }$. To determine whether an $(r+s)$-tuple $\mathfrak{C}$ in ${\mathbb{F}}_q{(\theta )}^{r+s}$ gives a shuffle relation, we relate it to the ${\mathbb{F}}_q[t]$-torsion property of the point ${\mathbf{v}}_{\mathfrak{C}}\in E^{\prime }({\mathbb{F}}_q[\theta ])$ constructed with respect to the given $(r+s)$-tuple $\mathfrak{C}$. We also provide an effective criterion for deciding the ${\mathbb{F}}_q[t]$-torsion property of the point ${\mathbf{v}}_{\mathfrak{C}}$.

Thakur [Tha10] 表明，对于r，$秒\in \mathbb{N}$, 两个 Carlitz zeta 值的乘积 ${\zeta }_{\mathrm{一种}}(r)$ 和 ${\zeta }_{\mathrm{一种}}(秒)$ 可以表示为 ${\mathbb{F}}_p$- 线性组合 ${\zeta }_{\mathrm{一种}}(r+秒)$ 和双 zeta 重量值 $r+秒$. 这样的表达式被 Thakur 称为 shuffle 关系。固定r ,$秒\in \mathbb{N}$, 我们构造了一个t模${乙}^{\prime }$. 确定一个$(r+秒)$-元组 $\mathfrak{C}$ 在 ${\mathbb{F}}_q{(\theta )}^{r+秒}$ 给出了一个混洗关系，我们将它与 ${\mathbb{F}}_q[吨]$- 点的扭转特性 ${\mathbf{v}}_{\mathfrak{C}}\in {乙}^{\prime }({\mathbb{F}}_q[\theta ])$ 相对于给定的构造 $(r+秒)$-元组 $\mathfrak{C}$. 我们还提供了一个有效的标准来决定${\mathbb{F}}_q[吨]$- 点的扭转特性 ${\mathbf{v}}_{\mathfrak{C}}$.