All Questions

Let $r\leq n$ and $d$ be positive integers. A probability vector is a vector of non-negative entries that sum to 1. For each probability vector $\lambda$ of length $n$, let $$s(\lambda)=(\dim[\pi] \...

The convex polytope flag vector ring $\mathcal{R}$ satisfies the cone product formula $$ C(U) C(V) = C(J(U, V)) + DUV $$ where $$ J(U, V) = U C(V) + C(U) V - e_1 UV $$ is the join formula. Note: ...

The Kostant partition function is known to be related to volumes and Ehrhart polynomials of flow polytopes of graphs (see e.g. https://link.springer.com/article/10.1007/s00031-008-9019-8 or https://...

On page 13 of "Tilting modules for the Auslander algebra of $K(x)/x^n$" the author, Geuenich, suggests that the number ($p_{n,i}$) of isomorphism classes of modules, occurring as the $i$-th summand of ...

Let $\Phi$ be a crystallographic root system in an $n$-dimensional Euclidean vector space $(V,\langle\cdot,\cdot\rangle)$. For a root $\alpha\in \Phi$ we use $\alpha^\vee := \frac{2}{\langle \alpha,\...