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 Order## Explore 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

Transposition## Cite this as:

Weisstein, Eric W. "Transposition." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Transposition.html