You are here
Home ›transposition
Primary tabs
transposition
Given a finite set , a transposition is a permutation (bijective function of onto itself) such that there exist indices such that , and for all other indices . This is often denoted (in the cycle notation) as .
One of the main results on symmetric groups states that any permutation can be expressed as composition (product) of transpositions, and for any two decompositions of a given permutation, the number of transpositions is always even or always odd.
Related:
Cycle2, SignatureOfAPermutation
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:
Mathematics Subject Classification
03-00 General reference works (handbooks, dictionaries, bibliographies, etc.)05A05 Permutations, words, matrices
20B99 None of the above, but in MSC2010 section 20Bxx
- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)
- Other useful stuff
Recent Activity
Jun 15
new question: Sorry to steal a few minutes of your time for this question, but i honestly don't know what else to do. by Whrazithar
new question: equality of the determinants of submatrices of an orthogonal matrix by ismayli
Jun 11
new correction: Typo by suitangi
Jun 2
new question: Creating another set with same cardinality. by hkkass
Jun 1
new image: ProblemOneRevised by unlord
new Education: Chapter II by rspuzio
May 31
new collection: The Calculus by Davis and Brenke by rspuzio
new question: Proofs by weixifan
new question: Summation Integration Question by trevor.nickle
May 27
new correction: typo+finite measure hypothesis by Filipe
new question: Sorry to steal a few minutes of your time for this question, but i honestly don't know what else to do. by Whrazithar
new question: equality of the determinants of submatrices of an orthogonal matrix by ismayli
Jun 11
new correction: Typo by suitangi
Jun 2
new question: Creating another set with same cardinality. by hkkass
Jun 1
new image: ProblemOneRevised by unlord
new Education: Chapter II by rspuzio
May 31
new collection: The Calculus by Davis and Brenke by rspuzio
new question: Proofs by weixifan
new question: Summation Integration Question by trevor.nickle
May 27
new correction: typo+finite measure hypothesis by Filipe
Attached Articles
Corrections
two things by matte ✓


