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Let $\mathbb{N}$ denote the set of positive integers. We define a relation $R \subseteq \mathbb{N}^4$ in the following way: $(p,q,n,s)\in R$ if and only if there is $S\subseteq [0,1]^n$ with $|S| = s …

Let $T\neq \emptyset$ be a finite subset of $\mathbb{Z}\times\mathbb{Z}$. We say that $\mathbb{Z}^2 = \mathbb{Z}\times\mathbb{Z}$ is parquettable by $T$ if there is a partition $\frak P$ of $\mathbb{Z …

Let $\{0,1\}^{<\omega}$ denote the collection of finite binary sequences. By a hash function we mean a computable map $$h: \{0,1\}^{<\omega} \to \{0,1\}^n$$ for some fixed $n\in\omega$. Define $\text{ …

The "mortal matrix" problem: Given a set of $n\times n$-matrices with integer entries, decide whether they can be multiplied, in any order and possibly with repetition, to give the $0$-matrix. If I re …