A sweep of a point configuration is any ordered partition induced by a linear functional. Posets of sweeps of planar point configurations were formalized and abstracted by Goodman and Pollack under the theory of allowable sequences of permutations. We introduce two generalizations that model posets of sweeps of higher dimensional configurations. Sweeps of a point configuration are in bijection with faces of an associated sweep polytope. Mimicking the fact that sweep polytopes are projections of permutahedra, we define sweep oriented matroids as strong maps of the braid oriented matroid. Allowable sequences are then the sweep oriented matroids of rank 2, and many of their properties extend to higher rank. We show strong ties between sweep oriented matroids and both modular hyperplanes and Dilworth truncations from (unoriented) matroid theory. Pseudo-sweeps are a generalization of sweeps in which the sweeping hyperplane is allowed to slightly change direction, and that can be extended to arbitrary oriented matroids in terms of cellular strings. We prove that for sweepable oriented matroids, sweep oriented matroids provide a sphere that is a deformation retract of the poset of pseudo-sweeps. This generalizes a property of sweep polytopes (which can be interpreted as monotone path polytopes of zonotopes), and solves a special case of the strong Generalized Baues Problem for cellular strings. A second generalization are allowable graphs of permutations: symmetric sets of permutations pairwise connected by allowable sequences. They have the structure of acycloids and include sweep oriented matroids.

点配置的扫描是由线性泛函引起的任何有序划分。 Goodman 和 Pollack 在允许的排列序列理论下对平面点配置的扫描偏集进行了形式化和抽象化。我们引入了两种对高维配置的扫描偏序集进行建模的概括。点配置的扫描与相关扫描多面体的面双射。模仿扫描多面体是置换面体的投影这一事实，我们将扫描定向拟阵定义为辫状定向拟阵的强映射。允许的序列是 2 阶的扫描导向拟阵，并且它们的许多属性扩展到更高的阶。我们展示了扫描导向拟阵与模超平面和（无向）拟阵理论的迪尔沃斯截断之间的紧密联系。伪扫描是扫描的推广，其中允许扫描超平面稍微改变方向，并且可以根据单元串扩展到任意方向的拟阵。我们证明，对于可扫描定向拟阵，扫描定向拟阵提供了一个球体，该球体是伪扫描偏序集的变形缩回。这概括了扫描多胞形的性质（可以解释为带位胞的单调路径多胞形），并解决了细胞串的强广义波埃斯问题的特殊情况。第二个概括是允许的排列图：通过允许的序列成对连接的对称排列集。它们具有非摆线结构并包括扫掠定向拟阵。