English

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 πSn\pi \in S_n 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 π\pi and the modular decomposition of its inversion graph. We also consider the special case of multiplicative decompositions.

Keywords

Cite

@article{arxiv.1111.3419,
  title  = {Decomposing Sets of Inversions},
  author = {Lukas Katthän},
  journal= {arXiv preprint arXiv:1111.3419},
  year   = {2013}
}
R2 v1 2026-06-21T19:36:09.111Z