Discretized configurations and partial partitions
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- by Aaron Abrams, David Gay and Valerie Hower PDF
- Proc. Amer. Math. Soc. 141 (2013), 1093-1104 Request permission
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 $\{1,\dots ,n+1\}$ 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.References
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Additional Information
- Aaron Abrams
- Affiliation: Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California 94720
- Address at time of publication: Department of Mathematics, Robinson Hall, Washington and Lee University, Lexington, Virginia 24450
- Email: abrams.aaron@gmail.com
- David Gay
- Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
- MR Author ID: 686652
- Email: d.gay@euclidlab.org
- Valerie Hower
- Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
- Address at time of publication: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
- Email: vhower@math.berkeley.edu, vhower@math.miami.edu
- Received by editor(s): September 15, 2010
- Received by editor(s) in revised form: July 21, 2011
- Published electronically: July 17, 2012
- Communicated by: Ken Ono
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1093-1104
- MSC (2010): Primary 55R80, 05A18, 11B73
- DOI: https://doi.org/10.1090/S0002-9939-2012-10816-0
- MathSciNet review: 3003699