All Questions

I was fascinated by the solutions of Problem 8 of the IMC 2021 contest, which can be summarized as: Theorem 1. Let $v_1,\dotsc,v_N$ be distinct unit vectors in $\mathbb{R}^n$ such that among any three ...

I am trying to find a reference for the following fact. It is elementary and not hard to prove, but I haven't been able to find the question treated anywhere. Let $A$ be an $l\times n$ matrix with ...

The Affine Degeneracy problem is about deciding whether $n$ given points in $\mathbb{R}^d$ (or $\mathbb{Q}^d$) are "in general position". i.e. there is no $d+1$ tuple of points which lies in ...

I'm looking for combinatorial proofs of the convolutional identity COP below and its specializations I) and II). (Edit 6/2/2023: A combinatorial proof is sketched in a blog post by Mike Spivey of a ...

I'm working on a problem related to $\textbf{Randell's isotopy theorem}$ for complex hyperplane arrangements. I have a question which seems quite obvious. However, I haven't found a rigorous proof ...