2 problems

Let $\mathfrak H=\mathbf Q\langle x,y\rangle$, with shuffle multiplication (denoted by juxtaposition with the shuffle symbol) and harmonic multiplication $*$. Let $\mathfrak H^0$ b…

Let $P$ be a lattice polytope, and let ${\mathcal H}_P\subseteq\mathbb{R}[y_0,\mathbf{y}]$ be its harmonic algebra, with bigraded ideal $\overline{{\mathcal H}}_P$. Harmonic algebr…