The conflated expression graph for an arbitrary permutation
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917550828290048 |
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| author | Zhu, Jieru |
| author_facet | Zhu, Jieru |
| 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 $ρ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00961 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The conflated expression graph for an arbitrary permutation Zhu, Jieru Combinatorics Representation Theory 05E16 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 $ρ$. |
| title | The conflated expression graph for an arbitrary permutation |
| topic | Combinatorics Representation Theory 05E16 |
| url | https://arxiv.org/abs/2606.00961 |