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arXiv · 1401.5568

On the group of alternating colored permutations

Eli Bagno·David Garber·Toufik Mansour
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Abstract

The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product $\mathbb{Z}_r \wr S_n$. We present a 'Coxeter-like' presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of $\mathbb{Z}_{\frac{r}{2}} \wr S_n$ and use this point of view to give another expression for the length function. We also use this covering to lift several known parameters of $\mathbb{Z}_{\frac{r}{2}} \wr S_n$ to the group of alternating colored permutations.

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Eli Bagno, David Garber, Toufik Mansour. 2014-01-22. On the group of alternating colored permutations. https://arxiv.org/abs/1401.5568

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