Before revision:  In addition, the concept of nested canalization is further generalized and closed formulas for the number of such generalized functions , as well as for the number of equivalence classes  under permutation of variables , are derived. The latter is motivated by the fact that two nested canalizing functions that differ only by a permutation of the variables share many important properties .
After revision:  In addition, the concept of nested canalization is further generalized and closed formulas for the number of such generalized functions , as well as for the number of equivalence classes under permutation of variables . Together, the results of the paper represent a useful mathematical framework for the study of NCFs and their dynamic networks .