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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.04053 |
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| _version_ | 1866914178945515520 |
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| author | Chou, Jack Chen-An Setiabrata, Linus |
| author_facet | Chou, Jack Chen-An Setiabrata, Linus |
| contents | We find a layered permutation $w\in S_n$ whose Schubert polynomial $\mathfrak S_w(x_1, \dots, x_n)$ has support of size asymptotically at least $n!/4^n$. This gives precise asymptotics for the growth rate of $β(n):= \max_{w\in S_n}|\mathrm{supp}(\mathfrak S_w)|$. We find a different layered permutation $w\in S_n$ whose Grothendieck polynomial has support of size asymptotically at least $n!/e^{\sqrt{2n} \cdot \ln(n)}$ and obtain more precise asymptotics for the growth rate of $β^{\mathfrak G}(n):=\max_{w\in S_n}|\mathrm{supp}(\mathfrak G_w)|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically maximal Schubitopes Chou, Jack Chen-An Setiabrata, Linus Combinatorics We find a layered permutation $w\in S_n$ whose Schubert polynomial $\mathfrak S_w(x_1, \dots, x_n)$ has support of size asymptotically at least $n!/4^n$. This gives precise asymptotics for the growth rate of $β(n):= \max_{w\in S_n}|\mathrm{supp}(\mathfrak S_w)|$. We find a different layered permutation $w\in S_n$ whose Grothendieck polynomial has support of size asymptotically at least $n!/e^{\sqrt{2n} \cdot \ln(n)}$ and obtain more precise asymptotics for the growth rate of $β^{\mathfrak G}(n):=\max_{w\in S_n}|\mathrm{supp}(\mathfrak G_w)|$. |
| title | Asymptotically maximal Schubitopes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.04053 |