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  "path": "/abs/2604.04097v1",
  "publishedAt": "2026-04-07T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Sandro M. Roch"
  ],
  "textContent": "**Authors:** Sandro M. Roch\n\nA 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"
}