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My answer concerns Question 2. When I was dealing with the system for $n=4$ I noticed that we can split it as follows (unfortunately, I failed to obtain essential advances from this observation). Let …

Recently I attacked this combinatorial question. The value of $m(n)$ introduced in it equals to a clique cover number of a generalized Kneser graph $KG_{n,4,1}=K(n,4,2)$ (or the chromatic number of it …

Peter Mueller provided a negative answer for $n=4$. Based on it, we show that the answer is negative for any even $n\ge 4$. Indeed, suppose for a contradiction that the space $V=\mathbb R^n$ admits a …

According to [p. 8], Baranyai's theorem [B] implies that the vertex set of the Kneser graph $K(n,k)$ can be partitioned into $\left\lceil\frac{\binom{n}{k}}{\left\lfloor\frac{n}{k}\right\rfloor}\righ …

This question is a sequel of my last question and is eventually motivated by recent advances in quantum physics. Given an even number $n\ge 6$ and a positive integer $k<n$, Claim from the linked quest …