# The real tau-conjecture is true on average

@article{Briquel2020TheRT,
title={The real tau-conjecture is true on average},
author={Ir{\'e}n{\'e}e Briquel and Peter B{\"u}rgisser},
journal={ArXiv},
year={2020},
volume={abs/1806.00417}
}
• Published 1 June 2018
• Computer Science, Mathematics
• ArXiv
Koiran's real $\tau$-conjecture claims that the number of real zeros of a structured polynomial given as a sum of $m$ products of $k$ real sparse polynomials, each with at most $t$ monomials, is bounded by a polynomial in $m,k,t$. This conjecture has a major consequence in complexity theory since it would lead to superpolynomial bounds for the arithmetic circuit size of the permanent. We confirm the conjecture in a probabilistic sense by proving that if the coefficients involved in the… Expand
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• SIAM J. Appl. Algebra Geom.
• 2019
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• Mathematics, Computer Science
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• 2021
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• 2019
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