N-homogeneous superalgebras

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