Counterexamples to Robichaux's conjecture for Grothendieck polynomials
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910281881354240 |
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| author | Dizier, Avery St. |
| author_facet | Dizier, Avery St. |
| contents | Ross and Yong conjectured a $K$-theoretic Kohnert rule for Grothendieck polynomials. Robichaux exhibited a counterexample to the Ross--Yong rule and proposed a revised ghost $K$-Kohnert rule, proving both rules hold for 321-avoiding permutations. We provide counterexamples to Robichaux's rule and give an explicit bijection showing that both the Ross--Yong and Robichaux rules hold for 1432-avoiding permutations. As an application, we provide a Kohnert-theoretic characterization of 1432-avoidance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02257 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counterexamples to Robichaux's conjecture for Grothendieck polynomials Dizier, Avery St. Combinatorics 05E05 Ross and Yong conjectured a $K$-theoretic Kohnert rule for Grothendieck polynomials. Robichaux exhibited a counterexample to the Ross--Yong rule and proposed a revised ghost $K$-Kohnert rule, proving both rules hold for 321-avoiding permutations. We provide counterexamples to Robichaux's rule and give an explicit bijection showing that both the Ross--Yong and Robichaux rules hold for 1432-avoiding permutations. As an application, we provide a Kohnert-theoretic characterization of 1432-avoidance. |
| title | Counterexamples to Robichaux's conjecture for Grothendieck polynomials |
| topic | Combinatorics 05E05 |
| url | https://arxiv.org/abs/2606.02257 |