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Principal Möbius function values for permutations under classic pattern containment

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posted on 09.10.2018 by David Marchant
These files have the value of the principal Möbius function \mu[1, \pi] for all canonical permutations with length 12 or less.

A permutation is canonical if, amongst the symmetries of the permutation, it has smallest lexicographic order.

Each line contains the permutation, the number of symmetries, and the value of the principal Möbius function, separated by semi-colons. For example,

{1,3,2} ; 4 ; -1

tells us that the permutation 132 has four symmetries, and that the value of the principal Möbius function is -1.




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