Discretized configurations and partial partitions

Aaron Abrams; David Gay; Valerie Hower

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arXiv · 1009.2935

Discretized configurations and partial partitions

Aaron Abrams·David Gay·Valerie Hower

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Abstract

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 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.

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Aaron Abrams, David Gay, Valerie Hower. 2010-09-15. Discretized configurations and partial partitions. https://arxiv.org/abs/1009.2935

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