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Orbit of Permutation

Let

Thus above defined relation

**ƒ**be any permutation on a set**S**. If a relation**~**is defined on**S**such that**a ~ b ƒ(n) (a) = b**for some integer**n**and**∀ a, b S**, we observe that the relation**‘~’**is**Reflexive, because**

(i)(i)

**a ~ a ƒ(n) (a) = I (a) = a ∀ a S**.**(ii)**Symmetric, because**a ~ b ƒ(n) (a) = b**for some integer**n****a = ƒ(n) (b) b – a for a, b S**.**(iii)**Transitive, because**a ~ b**and**b ~ c****ƒ(n) (a) = b, ƒ(m) (b) = c**for some integers**n**and**m**.**ƒ**_{m}(ƒn (a)) = ƒ_{m}(b) = c**ƒ**for some integer_{m+n}(a) = c**(m + n) a ~ c**.Thus above defined relation

**~**is an equivalence relation on**S**and hence it partitions**S**into mutually disjoint classes. Each equivalence class determined by the above relation is called an orbit of**ƒ**.**Services: -**Orbit of Permutation Homework | Orbit of Permutation Homework Help | Orbit of Permutation Homework Help Services | Live Orbit of Permutation Homework Help | Orbit of Permutation Homework Tutors | Online Orbit of Permutation Homework Help | Orbit of Permutation Tutors | Online Orbit of Permutation Tutors | Orbit of Permutation Homework Services | Orbit of PermutationSubmit Your Query ???

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