Decomposing Sets of Inversions
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.
1978 ◽
Vol 36
(1)
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pp. 492-493
2016 ◽
Vol 32
(3)
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pp. 204-214
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2019 ◽
Vol 3
(4)
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pp. 209-222
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