4 problems

Let $\Phi^+$ be a unimodular positive root system, let ${\mathfrak t}$ be the ambient real vector space, and let $R(x)$ denote the associated $R$-polynomial. Positivity conjecture.…

Let $X$ be a list of vectors, and let $\cal{P}_-(X)$ denote the internal polynomial space. For each sublist $Y\subseteq X$, let $p_Y$ be the associated polynomial, and say that a s…

Let $f(x)$ be a spline satisfying a refinement equation with coefficients $c_j$, dilation factor $\lambda$, and shifts $d_j$, and suppose that $\sum_{j=0}^N c_j=\lambda$. Let…

Let $X$ be a unimodular list of vectors, let $Z(X)$ be its zonotope, and let ${\cal Z}_-(X)$ be the set of integer points in the interior of $Z(X)$. Let $M_X$ be the box spline ass…