Signotopes Induce Unique Sink Orientations on Grids
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913006770716672 |
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| author | Roch, Sandro M. |
| author_facet | Roch, Sandro M. |
| contents | A unique sink orientation (USO) is an orientation of the edges of a polytope in which every face contains a unique sink. For a product of simplices $Δ_{m-1} \times Δ_{n-1}$, Felsner, Gärtner and Tschirschnitz (2005) characterize USOs which are induced by linear functions as the USOs on a $(m \times n)$-grid that correspond to a two-colored arrangement of lines. We generalize some of their results to products $Δ^1 \times\cdots\times Δ^r$ of $r$ simplices, USOs on $r$-dimensional grids and $(r+1)$-signotopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Signotopes Induce Unique Sink Orientations on Grids Roch, Sandro M. Computational Geometry Combinatorics 52C40, 52C30 I.3.5; G.2.1; F.2.2 A unique sink orientation (USO) is an orientation of the edges of a polytope in which every face contains a unique sink. For a product of simplices $Δ_{m-1} \times Δ_{n-1}$, Felsner, Gärtner and Tschirschnitz (2005) characterize USOs which are induced by linear functions as the USOs on a $(m \times n)$-grid that correspond to a two-colored arrangement of lines. We generalize some of their results to products $Δ^1 \times\cdots\times Δ^r$ of $r$ simplices, USOs on $r$-dimensional grids and $(r+1)$-signotopes. |
| title | Signotopes Induce Unique Sink Orientations on Grids |
| topic | Computational Geometry Combinatorics 52C40, 52C30 I.3.5; G.2.1; F.2.2 |
| url | https://arxiv.org/abs/2604.04097 |