An exchange of two elements of an ordered list with all others staying the same. A transposition is therefore a permutation of two
elements. For example, the swapping of 2 and 5 to take the list 123456 to 153426
is a transposition. The permutation symbol 
is defined as 
, where 
is the number of transpositions of pairs of elements that
must be composed to build up the permutation.
Transposition
See also
Inversion Number, Permutation, Permutation Symbol, Transposition Graph, Transposition OrderExplore with Wolfram|Alpha
References
Skiena, S. "Permutations from Transpositions." §1.1.4 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 9-11, 1990.Referenced on Wolfram|Alpha
TranspositionCite this as:
Weisstein, Eric W. "Transposition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Transposition.html