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arXiv · 2104.00838

A condition for the existence of zero coefficients in the powers of the determinant polynomial

Minoru Itoh·Jimpei Shimoyoshi
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Abstract

We discuss the existence of zero coefficients in the powers of the determinant polynomial of order $n$. D. G. Glynn proved that the coefficients of the $m$th power of the determinant polynomial are all nonzero, if $m = p-1$ with a prime $p$. We show that the converse also holds, if $n \geq 3$. The proof is quite elementary.

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Minoru Itoh, Jimpei Shimoyoshi. 2021-04-02. A condition for the existence of zero coefficients in the powers of the determinant polynomial. https://doi.org/10.1016/j.jalgebra.2021.03.017

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