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Full-Text Articles in Mathematics
On The Topology Of The Permutation Pattern Poset, Peter R. W. Mcnamara, Einar Steingrímsson
On The Topology Of The Permutation Pattern Poset, Peter R. W. Mcnamara, Einar Steingrímsson
Faculty Journal Articles
The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus not shellable. Nevertheless, there seem to be large classes of intervals that are shellable and thus have the homotopy type of a wedge of spheres. We prove this to be the case for all intervals of layered permutations that have no disconnected subintervals of rank 3 or more. We also characterize in a simple way …