@misc{Lutz2006, author = {Lutz, Frank H.}, title = {Enumeration and Random Realization of Triangulated Surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9012}, number = {06-07}, year = {2006}, abstract = {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 geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.}, language = {en} } @misc{Lutz2006, author = {Lutz, Frank H.}, title = {Triangulated Manifolds with Few Vertices: Combinatorial Manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9028}, number = {06-08}, year = {2006}, abstract = {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, we give a list of all known examples of vertex-minimal triangulations.}, language = {en} } @misc{KoehlerLutz2006, author = {K{\"o}hler, Ekkehard G. and Lutz, Frank H.}, title = {Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9031}, number = {06-09}, year = {2006}, abstract = {We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial \$d\$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on \$n\leq 13\$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.}, language = {en} } @misc{CsorbaLutz2006, author = {Csorba, Peter and Lutz, Frank H.}, title = {Graph Coloring Manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9043}, number = {06-11}, year = {2006}, abstract = {We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lov\ยด{a}sz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of highly connected, highly symmetric manifolds.}, language = {en} } @misc{HougardyLutzZelke2006, author = {Hougardy, Stefan and Lutz, Frank H. and Zelke, Mariano}, title = {Polyhedra of Genus 2 with 10 Vertices and Minimal Coordinates}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9054}, number = {06-12}, year = {2006}, abstract = {We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.}, language = {en} } @misc{HougardyLutzZelke2006, author = {Hougardy, Stefan and Lutz, Frank H. and Zelke, Mariano}, title = {Polyhedra of Genus 3 with 10 Vertices and Minimal Coordinates}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9064}, number = {06-13}, year = {2006}, abstract = {We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.}, language = {en} } @misc{Lutz2006, author = {Lutz, Frank H.}, title = {Combinatorial 3-Manifolds with 10 Vertices}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9071}, number = {06-14}, year = {2006}, abstract = {We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product \$S^2 x S^1\$ and 615 triangulations of the twisted sphere product \$S^2 \underline{x} S^1\$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.}, language = {en} } @misc{Lutz2003, author = {Lutz, Frank H.}, title = {Triangulated Manifolds with Few Vertices: Geometric 3-Manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7583}, number = {03-36}, year = {2003}, abstract = {We explicitly construct small triangulations for a number of well-known \$3\$-dimensional manifolds and give a brief outline of some aspects of the underlying theory of \$3\$-manifolds and its historical development.}, language = {en} } @misc{Lutz2003, author = {Lutz, Frank H.}, title = {Small Examples of Non-Constructible Simplicial Balls and Spheres}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7500}, number = {03-28}, year = {2003}, abstract = {We construct non-constructible simplicial \$d\$-spheres with \$d+10\$ vertices and non-constructible, non-realizable simplicial \$d\$-balls with \$d+9\$ vertices for \$d\geq 3\$.}, language = {en} } @misc{JoswigLutz2004, author = {Joswig, Michael and Lutz, Frank H.}, title = {One-Point Suspensions and Wreath Products of Polytopes and Spheres}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7836}, number = {04-08}, year = {2004}, abstract = {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 simplicial complexes with a various interesting combinatorial and topological properties. In particular, infinitely many non-PL spheres as well as contactible simplicial complexes with a vertex-transitive group of automorphisms cab be contained in this way.}, language = {en} } @misc{Lutz2004, author = {Lutz, Frank H.}, title = {Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7863}, number = {04-11}, year = {2004}, abstract = {The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres with dihedral or cyclic symmetry on few vertices, and we present an infinite series of vertex-transitive nearly neighborly centrally symmetric 3-spheres.}, language = {en} }