Discretized Configurations and Partial Partitions
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چکیده
We show that the discretized configuration space of k points in the n-simplex is homotopy equivalent to a wedge of spheres of dimension n− k+1. This space is homeomorphic to the order complex of the poset of ordered partial partitions of {1, . . . , n+1} with exactly k parts. We also compute the Euler characteristic in two different ways, thereby obtaining a topological proof of a combinatorial recurrence satisfied by the Stirling numbers of the second kind.
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تاریخ انتشار 2010