Some results related to permanental inequalities

The FKG inequality and associated inequalities have been extensively studied in the literature. The FKG inequality has been extended to a 2m-function inequality which relates to some interesting permanental inequalities. In this paper, we prove some related inequalities and also give a simple alternative proof of the 2m-function inequality. Our proofs use tools of majorization theory and are thus based on a completely different approach than the usual one.