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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.09107 |
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| _version_ | 1866913987576201216 |
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| author | Chou, Jack Chen-An Setiabrata, Linus |
| author_facet | Chou, Jack Chen-An Setiabrata, Linus |
| contents | We show that the support of the Grothendieck polynomial $\mathfrak G_w$ of any fireworks permutation is as large as possible: a monomial appears in $\mathfrak G_w$ if and only if it divides $\mathbf x^{\mathrm{wt}(\overline{D(w)})}$ and is divisible by some monomial appearing in the Schubert polynomial $\mathfrak S_w$. Our formula implies that the homogenization of $\mathfrak G_w$ has M-convex support. We also show that for any fireworks permutation $w\in S_n$, there exists a layered permutation $π(w)\in S_n$ so that $\mathrm{supp}(\mathfrak G_{π(w)})\supseteq \mathrm{supp}(\mathfrak G_w)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Newton polytopes of fireworks Grothendieck polynomials Chou, Jack Chen-An Setiabrata, Linus Combinatorics We show that the support of the Grothendieck polynomial $\mathfrak G_w$ of any fireworks permutation is as large as possible: a monomial appears in $\mathfrak G_w$ if and only if it divides $\mathbf x^{\mathrm{wt}(\overline{D(w)})}$ and is divisible by some monomial appearing in the Schubert polynomial $\mathfrak S_w$. Our formula implies that the homogenization of $\mathfrak G_w$ has M-convex support. We also show that for any fireworks permutation $w\in S_n$, there exists a layered permutation $π(w)\in S_n$ so that $\mathrm{supp}(\mathfrak G_{π(w)})\supseteq \mathrm{supp}(\mathfrak G_w)$. |
| title | Newton polytopes of fireworks Grothendieck polynomials |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.09107 |