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Let $h= (H_0, H_1, ..., H_n)$ be the vector of the first $n+1$ Hermite functions. We give a complete characterization of all lattices $\\Lambda \\subseteq \\bR ^2$ such that the Gabor system\n  $\\{e^{2\\pi i \\lambda_2 t} \\boh (t-\\lambda_1): \\lambda = (\\lambda_1, \\lambda_2) \\in \\Lambda \\}$ is a frame for $L^2 (\\bR, \\bC ^{n+1})$. 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