Upper bounds for the monotone rank of the unique disjointness matrix

Igor S. Sergeev

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arXiv · 2607.27014

Upper bounds for the monotone rank of the unique disjointness matrix

Igor S. Sergeev

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Abstract

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.

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BibTeX RIS

Igor S. Sergeev. 2026-07-29. Upper bounds for the monotone rank of the unique disjointness matrix. https://arxiv.org/abs/2607.27014

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