A polynomial basis for the multizeta algebra in positive characteristic

Let $K=\mathbb{F}_q(θ)$, and let $\mathcal{Z}$ be the $K$-algebra generated by Thakur's multiple zeta values $ζ_A(\mathfrak{s})$. We prove that $\mathcal{Z}$ is a polynomial algebra and construct an explicit polynomial basis of $\mathcal{Z}$ over $K$. We also determine the transcendence degree of $K