Chebyshev type inequalities involving permanents and their applications

We extend the well-known Chebyshev’s inequality to some new cases involving permanents under the proper hypotheses. Our main results areper(A⊙B)n!⩾perAn!·perBn!andperA∏i=1n∑j=1nai,j⩽perB∏i=1n∑j=1nbi,j.As applications, we consider the problem of finding bounds of the ratios of two functions involving permanents.