  We develop the theory of N-homogeneous algebras in a super setting, with
particular emphasis on the Koszul property. To any Hecke operator on a vector
superspace, we associate certain superalgebras and generalizing the ordinary
symmetric and Grassmann algebra, respectively. We prove that these algebras are
N-Koszul. For the special case where the Hecke operator is the ordinary
supersymmetry, we derive an $N$-generalized super-version of MacMahon's
classical "master theorem".
