Decomposing sets of inversions (Q1953426)

Summary: In this paper we consider the question how the set of inversions of a permutation \(\pi \in S_n\) can be partitioned into two subsets, which are themselves inversion sets of permutations in \(S_n\). Our method is to study the modular decomposition of the inversion graph of \(\pi\). A correspondence to the substitution decomposition of \(\pi\) is also given. Moreover, we consider the special case of multiplicative decompositions.