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A matrix AA is said to have the displacement structure if the rank of the Sylvester displacement AU−VAAU-VA or the Stein displacement A−VAUA-VAU is much smaller than the rank of AA. In this article, we study the displacement structure of the DMP inverse Ad,†{A}^{d,\dagger }. Estimations for the Sylvester displacement rank of DMP inverse are presented under some restrictions. The generalized displacement is also discussed. The general results are applied to the core inverse.