signature of a permutation (original) (raw)
Proof: This is clear if g is the identity map
X→X. If g is any other permutation, then for some_consecutive_ a,b∈X we have a<b and g(a)>g(b). Let h∈Gbe the transposition of a and b. We have
| k(g∘h) | = | k(g)-1 |
|---|---|---|
| χ(g∘h) | = | -χ(g) |
and the proposition follows by induction on k(g).
| Title | signature of a permutation |
|---|---|
| Canonical name | SignatureOfAPermutation |
| Date of creation | 2013-03-22 13:29:19 |
| Last modified on | 2013-03-22 13:29:19 |
| Owner | rspuzio (6075) |
| Last modified by | rspuzio (6075) |
| Numerical id | 9 |
| Author | rspuzio (6075) |
| Entry type | Definition |
| Classification | msc 03-00 |
| Classification | msc 05A05 |
| Classification | msc 20B99 |
| Synonym | sign of a permutation |
| Related topic | Transposition |
| Defines | inversion |
| Defines | signature |
| Defines | parity |
| Defines | even permutation |
| Defines | odd permutation |