- #1

nomadreid

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Suppose one assumes a beginning ordered set of <1,2,3>

It is clear that (1,2) (2,3), and (1,3) are the adjacent transpositions for <1,2,3>

However, if I compose them (2,3)(1,2), I first apply the transposition (1,2) to <1,2,3> I now have <2,1,3> and now 2 and 3 are no longer neighbors. So is (2,3) still considered an adjacent transposition?

According the the definitions I find on the Internet, it appears that the answer is yes, but this goes contrary to the intuition of sapping neighbors at each step.

Thanks.