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D. Uminsky and K. Yeats [6] studied the properties of the log- operator L onthe subset of the finite symmetric sequences and prove the existence of aninfinite region R, bounded by parametrically de- fined hypersurfaces such thatany sequence corresponding a point of R is infinitely log concave. We study theproperties of a new operator L_r and redefine the hypersurfaces whichgeneralizes the one defined by Uminsky and Yeats [6]. We show that any sequencecorresponding a point of the region R, bounded by the new generalizedparametrically defined r-factor hypersurfaces, is Generalized r-factorinfinitely log concave. We also give an improved value of r_0 found by McNamaraand Sagan [4] as the log-concavity criterion using the new log-operator.

Infinite Log-Concavity and r-Factor