Discretized configurations and partial partitions

We show that the discretized configuration space of k-simplex is homotopy equivalent to a wedge of spheres of dimension n-k+1 \{1,\dots ,n+1\} parts. We compute the exponential generating function for the Euler characteristic of this space in two different ways, thereby obtaining a topological proof...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2013-03, Vol.141 (3), p.1093-1104
Main Authors: ABRAMS, AARON, GAY, DAVID, HOWER, VALERIE
Format: Article
Language:English
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Summary:We show that the discretized configuration space of k-simplex is homotopy equivalent to a wedge of spheres of dimension n-k+1 \{1,\dots ,n+1\} parts. We compute the exponential generating function for the Euler characteristic of this space in two different ways, thereby obtaining a topological proof of a combinatorial recurrence satisfied by the Stirling numbers of the second kind.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2012-10816-0