35 citations · 127 across the 21 of their papers we have counts for
14 papers · 1 filter
Hadamard Matrix Torsion
Davide Lofano, Frank H. Lutz
We construct a series HMT of -dimensional simplicial complexes with torsion HMT$(n))=(\mathbb{Z}_2)^{{k}\choose{1}} \times (\mathbb{Z}_4)^{{k}\choose{2}} \times \cdot…
Chromatic Numbers of Simplicial Manifolds
Frank H. Lutz, Jesper M. Møller
Higher chromatic numbers of simplicial complexes naturally generalize the chromatic number of a graph. In any fixed dimension , the -chromatic number of …
Extremal examples of collapsible complexes and random discrete Morse theory
Karim A. Adiprasito, Bruno Benedetti, Frank H. Lutz
We present extremal constructions connected with the property of simplicial collapsibility. (1) For each , there are collapsible (and shellable) simplicial -complexes w…
Knots in collapsible and non-collapsible balls
Bruno Benedetti, Frank H. Lutz
We construct the first explicit example of a simplicial 3-ball B_{15,66} that is not collapsible. It has only 15 vertices. We exhibit a second 3-ball B_{12,38} with 12 vertices tha…
Constructing Complicated Spheres
Mimi Tsuruga, Frank H. Lutz
Fast and efficient homology algorithms are in demand in the applied sciences for analyzing solid materials and proteins, processing digital imaging data, or pattern classification…
Stellar theory for flag complexes
Frank H. Lutz, Eran Nevo
Refining a basic result of Alexander, we show that two flag simplicial complexes are piecewise linearly homeomorphic if and only if they can be connected by a sequence of flag comp…
Equivelar and d-Covered Triangulations of Surfaces. II. Cyclic Triangulations and Tessellations
Frank H. Lutz
With the -family of cyclic triangulations we introduce a rich class of vertex-transitive triangulations of surfaces. In particular, there are infinite series of cyclic …
Equivelar and d-Covered Triangulations of Surfaces. I
Frank H. Lutz, Thom Sulanke, Anand K. Tiwari +1
We survey basic properties and bounds for -equivelar and -covered triangulations of closed surfaces. Included in the survey is a list of the known sources for -equivelar a…
f-Vectors of 3-Manifolds
Frank H. Lutz, Thom Sulanke, Ed Swartz
In 1970, Walkup completely described the set of -vectors for the four 3-manifolds , , , and . We improve one of Walkup's main restricti…
Isomorphism-free lexicographic enumeration of triangulated surfaces and 3-manifolds
Thom Sulanke, Frank H. Lutz
We present a fast enumeration algorithm for combinatorial 2- and 3-manifolds. In particular, we enumerate all triangulated surfaces with 11 and 12 vertices and all triangulated 3-m…
Graph coloring manifolds
Peter Csorba, Frank H. Lutz
We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lovasz. The class comprises examples of Stiefel manifolds, series of spheres and p…
Enumeration and random realization of triangulated surfaces
Frank H. Lutz
We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometr…
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…
Small examples of non-constructible simplicial balls and spheres
Frank H. Lutz
We construct non-constructible simplicial -spheres with vertices and non-constructible, non-realizable simplicial -balls with vertices for .