Let P_(n,k) denote the set of all polynomials of degree at most n with real coefficients and with at most k (0 ≤ k ≤ n) zeros in the open unit disk. Let P_(n,k)~c denote the set of all polynomials of degree at most n with complex coefficients and with at most k (0 ≤ k ≤ n) zeros in the open unit disk. Let P_n (r) denote the set of all polynomials of degree at most n with real coefficients and with no zeros in the union of open disks with diameters [-1, -1 + 2r] and [1 - 2r, 1], respectively (0 < r ≤ 1). Let P_n~c(r) denote the set of all polynomials of degree at most n with complex coefficients and with no zeros in the union of open disks with diameters [-1, -1 +2r] and [1 - 2r, 1], respectively (0 < r ≤ 1).
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