  We study the Fredholm minors associated with a Fredholm equation of the
second type. We present a couple of new linear recursion relations involving
the $n$th and $n-1$th minors, whose solution is a representation of the $n$th
minor as an $n\times n$ determinant of resolvents. The latter is given a simple
interpretation in terms of a path integral over non-interacting fermions. We
also provide an explicit formula for the functional derivative of a Fredholm
minor of order $n$ with respect to the kernel. Our formula is a linear
combination of the $n$th and the $n\pm 1$th minors.
