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# Principal Möbius function values for permutations under classic pattern containment

Version 2 2018-10-09, 10:26

Version 1 2018-10-05, 13:13

dataset

posted on 2018-10-09, 10:26 authored by David MarchantDavid MarchantThese 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.