Abstract
The set S n of permutations form a group under composition, called the symmetric group. To this point we have hardly mentioned this fact, let alone exploited the group structure. The task of this chapter is to show how the combinatorial notions of inversion and descent can be understood as arising from the group structure. We will then generalize from the symmetric group to other finite groups with a similar structure, known as Coxeter groups. This gives a natural setting in which to give a more general notion of Eulerian numbers.
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Petersen, T.K. (2015). Coxeter groups. In: Eulerian Numbers. Birkhäuser Advanced Texts Basler Lehrbücher. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-3091-3_11
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DOI: https://doi.org/10.1007/978-1-4939-3091-3_11
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