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math.AC2021★ 2 cited
No short polynomials vanish on bounded rank matrices
Jan Draisma, Thomas Kahle, Finn Wiersig
We show that the shortest nonzero polynomials vanishing on bounded-rank matrices and skew-symmetric matrices are the determinants and Pfaffians characterising the rank. Algebraical…
math.AC2021★ 1 cited
Short polynomials in determinantal ideals
Thomas Kahle, Finn Wiersig
We show that a determinantal ideal generated by -minors does not contain any nonzero polynomials with or fewer terms. Geometrically this means that any nonzero polynomial…