  A new type of symmetry, ren-symmetry describing anyon physics and the
corresponding topological physics, is proposed. Ren-symmetry is a
generalization of super-symmetry which is widely applied in super-symmetric
physics such as the super-symmetric quantum mechanics, super-symmetric gravity,
super-symmetric string theory, super-symmetric integrable systems and so on.
The super-symmetry and Grassmann-number are, in some sense, the dual
conceptions, which turns out that these conceptions coincide for the ren
situation, that is, a similar conception of ren-number is devised to
ren-symmetry. In particular, some basic results of the ren-number and
ren-symmetry are exposed which allow one to derive, in principle, some new
types of integrable systems including ren-integrable models and ren-symmetric
integrable systems. Training examples of ren-integrable KdV type systems and
ren-symmetric KdV equations are explicitly given.
