All Questions

Let $A\subseteq V$ and $B\subseteq V^\star$ be spanning sets in a finite-dimensional real vector space $V$ and its dual $V^\star$. Suppose that $$ \langle b,a\rangle\in\lbrace0,1\rbrace $$ for all $a\...

I am working on an equation that would be solved if I show the following. Let $k \geq l$, and consider the set of $\{0,1\}$-matrices of size $k \times l$ with exactly $i$ 1’s. Consider the subset $\...

Given a vector $v\in\mathbb Z^n$ and pairwise commutative matrices $M_1,\dotsc,M_k\in \operatorname{SL}(n,\mathbb Z)$, how to compute all 01-vectors in the orbit of $v$ with respect to multiplication ...