On Chebotarëv's nonvanishing minors theorem and the Biró-Meshulam-Tao discrete uncertainty principle
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Chebotarëv's theorem says that every minor of a discrete Fourier matrix of prime order is nonzero. We prove a generalization of this result that includes analogues for discrete cosine and discrete sine matrices as special cases. We then establish a generalization of the Biró-Meshulam-Tao uncertainty principle to functions with symmetries that arise from certain group actions and twists. We then show that our result is best possible and always yields a lower bound at least as strong as Biró-Meshulam-Tao.
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