符号otope诱导独特的网格sink方向
Signotopes Induce Unique Sink Orientations on Grids
AI总结：
研究通过推广线性函数诱导的USO特性，探讨了r维网格和(r+1)符号otope上的USO结构特征。
摘要：
独特的sink方向（USO）是多面体边的定向，使得每个面包含唯一的sink。对于简单形乘积Δ_{m-1}×Δ_{n-1}，Felsner等人（2005）将由线性函数诱导的USO特征化为(m×n)网格上的二维线排列。本文推广了部分结果至r个简单形的乘积Δ^1×…×Δ^r，研究r维网格和(r+1)符号otope上的USO结构。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
