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arXiv · 2606.00961

The conflated expression graph for an arbitrary permutation

Jieru Zhu
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Abstract

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 $\rho$, we give an explicit method for producing a maximal chain containing $\rho$.

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Jieru Zhu. 2026-05-31. The conflated expression graph for an arbitrary permutation. https://arxiv.org/abs/2606.00961

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