Abstract
We find a new type of nonlinear supersymmetries, called [Formula: see text]-fold parasupersymmetry, which is a generalization of both [Formula: see text]-fold supersymmetry and parasupersymmetry. We provide a general formulation of this new symmetry and then construct a second-order [Formula: see text]-fold parasupersymmetric quantum system where all the components of [Formula: see text]-fold parasupercharges are given by type A [Formula: see text]-fold supercharges. We show that this system exactly reduces to the Rubakov–Spiridonov model when [Formula: see text] and admits a generalized type C [Formula: see text]-fold superalgebra. We conjecture the existence of other "[Formula: see text]-fold generalizations" such as [Formula: see text]-fold fractional supersymmetry, [Formula: see text]-fold orthosupersymmetry, and so on.
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