Chebyshev type inequalities involving permanents and their applications

Abstract We extend the well-known Chebyshev’s inequality to some new cases involving permanents under the proper hypotheses. Our main results are per ( A ⊙ B ) n ! ⩾ per A n ! · per B n ! and per A ∏ i = 1 n ∑ j = 1 n a i , j ⩽ per B ∏ i = 1 n ∑ j = 1 n b i , j . As applications, we consider the problem of finding bounds of the ratios of two functions involving permanents.