The M\"obius function of permutations with an indecomposable lower bound
Combinatorics
2018-10-15 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1710.03122,
title = {The M\"obius function of permutations with an indecomposable lower bound},
author = {Robert Brignall and David Marchant},
journal= {arXiv preprint arXiv:1710.03122},
year = {2018}
}
Comments
19 pages, 6 figures. Revised following comments from anonymous reviewers