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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00961 |
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Table of Contents:
- We show that the conflated expression graph for an arbitrary permutation has a unique minimal element and a unique maximal element, and every reduced expression sits on a maximal chain from the source to the sink. This generalizes the work of Manin-Schechtman regarding higher Bruhat orders, and gives an independent and self-contained proof of certain results in Hothem. In addition, we give explicit algorithms for elements in the top and bottom commutation classes. Given any reduced expression $ρ$, we give an explicit method for producing a maximal chain containing $ρ$.