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 epsilon_(ijk...) is defined as (-1)^n, where n is the number of transpositions of pairs of elements that must be composed to build up the permutation.

See also

Inversion Number, Permutation, Permutation Symbol, Transposition Graph, Transposition Order

Explore with Wolfram|Alpha


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


Cite this as:

Weisstein, Eric W. "Transposition." From MathWorld--A Wolfram Web Resource.

Subject classifications