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A linear gap for the maximal cp-rank

Contributed by Yair Lavi

We prove that the maximal cp-rank $p_n$ satisfies $p_n\ge n(n-3)/2$ for odd $n\ge5$ and $p_n\ge n(n-3)/2-1$ for even $n\ge6$ . Together with the known upper bound $p_n\le\binom{n+1}{2}-4$ , this gives $p_n=n^2/2+O(n)$ .

A mix of human-written and AI-generated textHuman understanding: all partsCompletely positive matrixCopositive matrixCyclic incidence matrixExposed facecp-rank

Nov 11, 20268 pages

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A linear gap for the maximal cp-rank

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