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. Mimicking the fact that sweep polytopes of point configurations (the monotone path polytopes of the associated zonotopes) 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. We also explore their connection with the generalized Baues problem for cellular strings, where sweep oriented matroids can play the role of monotone path polytopes, even for non-realizable oriented matroids. In particular, we show that for oriented matroids that admit a sweep oriented matroid, their poset of pseudo-sweeps deformation retracts to a sphere of the appropriate dimension. 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.

翻译：点配置的扫掠是由线性泛函诱导的任何有序划分。Goodman与Pollack在置换可允许序列理论中将平面点配置扫掠的偏序集形式化并抽象化。我们引入两种推广，以建模高维配置扫掠的偏序集。模拟点配置的扫掠多面体（相关带形多胞体的单调路径多胞体）是置换多面体的投影这一事实，我们将扫掠定向拟阵定义为辫子定向拟阵的强映射。此时可允许序列即为秩2的扫掠定向拟阵，其许多性质可推广至更高秩。我们展示了扫掠定向拟阵与（无向）拟阵理论中模超平面及迪尔沃思截断之间的紧密联系。我们还探讨了它们与胞腔弦的广义Baues问题的关联——在此问题中，扫掠定向拟阵可扮演单调路径多胞体的角色，甚至适用于不可实现的定向拟阵。特别地，我们证明：对于允许扫掠定向拟阵的定向拟阵，其伪扫掠偏序集形变收缩为适当维度的球面。第二个推广是置换可允许图：由可允许序列两两相连的置换的对称集合。它们具有无环图结构且包含扫掠定向拟阵。