The Möbius function of permutations with an indecomposable lower bound

Robert Brignall, David Marchant

Published 2017-10-09Version 1

We show that the M\"obius function of an interval in a permutation poset where the lower bound is sum (resp. skew) indecomposable depends solely on the sum (resp. skew) indecomposable permutations contained in the upper bound, and that this can simplify the calculation of the M\"obius sum. For increasing oscillations, we give a recursion for the M\"obius sum which only involves evaluating simple inequalities.