AI 中文总结
该研究给出唯一不相交矩阵的OR-秩上界，证明其与已知下界1.5ⁿ本质紧，还得到SUM-秩的上界1.89ⁿ，推进了矩阵秩相关问题的研究。
AI 中文摘要
研究表明，2ⁿ×2ⁿ唯一不相交矩阵的OR-秩（覆盖秩）为n^O(1)(3/2)ⁿ，因此已知的下界1.5ⁿ本质上是紧的；同时得到该矩阵的SUM-秩（划分秩）的上界为1.89ⁿ。
英文摘要
It is shown that the $\mathsf{OR}$-rank (covering rank) of the $2^n \times 2^n$ unique disjointness matrix is $n^{O(1)}(3/2)^n$, hence the known lower bound $1.5^n$ turns out to be essentially tight. By the way, an upper bound $1.89^n$ is obtained for the $\mathsf{SUM}$-rank (partition rank) of this matrix.
Comments7 pages (in English); 7 pages (in Russian)
