TITLE: Transposition decomposition of permutations?
QUESTION [5 upvotes]: Does there exist a reference table or software that gives the transposition decomposition of permutations in $S_n$ (for relatively small $n$ I suppose).

REPLY [2 votes]: A chemist showed this way to factor a permutation into transpositions. Draw n dots on each of two parallel lines in the plane. Connect the dots on one line with those on the other line by straight segments  according to the given permutation. There will be one  transposition for each intersection point of two segments. To see this slide one line over to the other allowing the dots to follow along their segments. The order of the dots is changed by a transposition when an intersection point is crossed. This provides a fast  mechanical way to compute the sign of a permutation , which was the motivation from theoretical chemistry.