Abstract
The elements of a finite nonempty partially ordered set are exposed at independent uniform times in to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's task is to choose online a maximal element. This generalizes the classical linear order secretary problem, for which it is known that the selector can succeed with probability and that this is best possible. We describe a strategy for the general problem that achieves success probability for an arbitrary partial order.
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