## Principal Möbius function values for permutations under classic pattern containment

dataset

posted on 09.10.2018 by David Marchant#### dataset

Datasets usually provide raw data for analysis. This raw data often comes in spreadsheet form, but can be any collection of data, on which analysis can be performed.

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.