Border symmetric rank conjecture for monomials

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Let x0,…,xnx_0,\ldots,x_n be variables and let 0≤α0≤⋯≤αn0\leq\alpha_0\leq\cdots\leq\alpha_n. Write bsrk⁡\operatorname{bsrk} for border symmetric rank. Border symmetric rank conjecture. For these exponents, one has

bsrk⁡(x0α0⋯xnαn)=∏i=0n−1(αi+1).\operatorname{bsrk}\left(x_0^{\alpha_0}\cdots x_n^{\alpha_n}\right)=\prod_{i=0}^{n-1}(\alpha_i+1).

The statement concerns the still-open problem of computing the border symmetric rank of monomials. The cited attribution is to Oeding (2016).

References

Primary source

Giorgio Ottaviani and Philipp Reichenbach, “Tensor Rank and Complexity”, arXiv:2004.01492 (2022).

Additional references

2 papers in this index state this conjecture (2019–2020). The statement above is taken from the most recent of them; the others are arXiv:1909.03811.

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