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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.12839 |
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Table of Contents:
- Let ${\mathcal W}_n$ denote any of the three families of classical Weyl groups: the symmetric groups ${\mathcal S}_n$, the hyperoctahedral groups (signed permutation groups) ${\mathcal S}^B_n$, or the even-signed permutation groups ${\mathcal S}^D_n$. In this paper we give an uniform construction of a Hamilton cycle for the restriction to involutions on these three families of groups with respect to a inverse-closed connecting set of involutions. This Hamilton cycle is optimal with respect to the Hamming distance only for the symmetric group ${\mathcal S}_n$. We also recall an optimal algorithm for a Gray code for type $B$ involutions. A modification of this algorithm would provide a Gray Code for type $D$ involutions with Hamming distance two, which would be optimal. We give such a construction for ${\mathcal S}^D_4$ and ${\mathcal S}^D_5$.