. . "In 1986 Lovasz, Spencer, and Vesztergombi proved a lower bound for the hereditary a discrepancy of a set system F in terms of determinants of square submatrices of the incidence matrix of F. As shown by an example of Hoffman, this bound can differ from herdisc(F) by a multiplicative factor of order almost log n, where n is the size of the ground set of F. We prove that it never differs by more than O((log n)^3/2), assuming |F| bounded by a polynomial in n. We also prove that if such an F is the union of t systems F_1, . . ., F_t, each of hereditary discrepancy at most D, then herdisc(F) \\leq O(t^(1/2)(log n)^(3/2) D). For t = 2, this almost answers a question of Sos. The proof is based on a recent algorithmic result of Bansal, which computes low-discrepancy colorings using semidefinite programming."@en . "http://arxiv.org/abs/1101.0767" . . . "[F7CD241F98A5]" . . "In 1986 Lovasz, Spencer, and Vesztergombi proved a lower bound for the hereditary a discrepancy of a set system F in terms of determinants of square submatrices of the incidence matrix of F. As shown by an example of Hoffman, this bound can differ from herdisc(F) by a multiplicative factor of order almost log n, where n is the size of the ground set of F. We prove that it never differs by more than O((log n)^3/2), assuming |F| bounded by a polynomial in n. We also prove that if such an F is the union of t systems F_1, . . ., F_t, each of hereditary discrepancy at most D, then herdisc(F) \\leq O(t^(1/2)(log n)^(3/2) D). For t = 2, this almost answers a question of Sos. The proof is based on a recent algorithmic result of Bansal, which computes low-discrepancy colorings using semidefinite programming." . "1"^^ . . "The determinant bound for discrepancy is almost tight" . . "10.1090/S0002-9939-2012-11334-6" . . . "10"^^ . . "000326515600009" . "I" . . "The determinant bound for discrepancy is almost tight"@en . "141" . . "0002-9939" . . "Matou\u0161ek, Ji\u0159\u00ED" . "RIV/00216208:11320/13:10172783!RIV14-MSM-11320___" . "RIV/00216208:11320/13:10172783" . . "The determinant bound for discrepancy is almost tight"@en . "Proceedings of the American Mathematical Society" . "The determinant bound for discrepancy is almost tight" . "2" . "11320" . "68809" . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "low-discrepancy colorings; incidence matrix; determinant bound; discrepancy"@en . "1"^^ . .