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.
See alsoInversion Number, Permutation, Permutation Symbol, Transposition Graph, Transposition Order
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ReferencesSkiena, 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.
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Weisstein, Eric W. "Transposition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Transposition.html