# name
Sweeps, Polytopes, Oriented Matroids, and Allowable Graphs of Permutations

# metadata.dc.description.abstract[].value
A sweep of a point configuration is any ordered partition induced by a linear func-  tional. 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 asso-  ciated 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 sweep-  ing 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

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Sweeps, Polytopes, Oriented Matroids, and Allowable Graphs of Permutations