Decomposing Sets of Inversions
Combinatorics
2013-02-27 v2
Abstract
In this note we consider the question how the set of inversions of a permutation can be partitioned into two subset, such that those are itself inversion sets of permutations. This is archived by exploiting a connection to a graph theoretical result. For this we establish a correspondence between the substitution decomposition of and the modular decomposition of its inversion graph. We also consider the special case of multiplicative decompositions.
Cite
@article{arxiv.1111.3419,
title = {Decomposing Sets of Inversions},
author = {Lukas Katthän},
journal= {arXiv preprint arXiv:1111.3419},
year = {2013}
}