514 citations
- Chemnitz University of TechnologyDE2 papers
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- Max-Born-Institute for Nonlinear Optics and Short Pulse SpectroscopyDE2 papers
- Weierstrass Institute for Applied Analysis and StochasticsDE2 papers
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- A. Alikhanyan National LaboratoryAM1 paper
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9 papers · 1 filter
Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
Frank H. Lutz
In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover,…
On the frontiers of polynomial computations in tropical geometry
Thorsten Theobald
We study some basic algorithmic problems concerning the intersection of tropical hypersurfaces in general dimension: deciding whether this intersection is nonempty, whether it is a…
On the number of Tverberg partitions in the prime power case
Stephan Hell
We give an extension of the lower bound of Vucic and Zivaljevic for the number of Tverberg partitions from the prime to the prime power case. Our proof is inspired by the Z_p-index…
One-Point Suspensions and Wreath Products of Polytopes and Spheres
Michael Joswig, Frank H. Lutz
It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicia…
Bier spheres and posets
Anders Björner, Andreas Paffenholz, Jonas Sjöstrand +1
In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n-2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices…
Box complexes, neighborhood complexes, and the chromatic number
Peter Csorba, Carsten Lange, Ingo Schurr +1
Lovasz's striking proof of Kneser's conjecture from 1978 using the Borsuk--Ulam theorem provides a lower bound on the chromatic number of a graph. We introduce the shore subdivisio…