Geodesic
Decomposing sets of inversions
Lukas Katthän1
1Philipps-Universität Marburg
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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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.
DOI : 10.37236/2609
Classification : 05A05, 52B12, 05E40
Mots-clés : inversion sets, permutation graphs, simple permutations, linear ordering polytope

Lukas Katthän  1

1 Philipps-Universität Marburg 
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     title = {Decomposing sets of inversions},
     journal = {The electronic journal of combinatorics},
     year = {2013},
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     doi = {10.37236/2609},
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Lukas Katthän. Decomposing sets of inversions. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2609

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