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Tweet 1

@AdonAlternative er, maybe that's not right. You can define the crossing number for s, #{(i,j) | i<j, s(i)>s(j)} without reference to representation and then see that a single transposition must either increase or decrease this. But then in the case of the cube it remains to show a single move is…

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Tweet 2

@AdonAlternative Now I'm wondering if you couldn't make a puzzle that would trick a mathematician into thinking odd sequences couldn't be identity but in fact every move is an element of An so they can.

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