Path integrals in finite sets

Erik G. F. Thomas

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Bicoloured Dyck paths and the contact polynomial for $n$ non-intersecting paths in a half-plane lattice.

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The Maximum Capacity Shortest Path Problem: Generation of Efficient Solution Sets

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Individual items of flow in a telecommunications or a transportation network may need to be separated by a minimum distance or time, called a “headway”. If link dependent, such restrictions in general have the effect that the minimum time path for a “convoy” of items to travel from a given origin to a given destination will depend on the size of the convoy. The Quickest Path problem seeks a path to minimise this convoy travel time. A closely related bicriterion problem is the Maximum...