@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{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{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} } @misc{Rambau2000, author = {Rambau, J{\"o}rg}, title = {Triangulierungen von Punktmengen und Polyedern}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6145}, number = {00-46}, year = {2000}, abstract = {Dieser Report wurde im Sommersemester 2000 an der TU Berlin in einer Spezialvorlesung {\"u}ber Triangulierungen von Punktmengen und Polyedern als Skriptum verwendet. Nach einem motivierenden Kapitel werden grundlegende Begriffe und Konstruktionen in der Theorie der Triangulierungen von Punktmengen und Polyedern vorgestellt. Danach werden als weiterf{\"u}hrende Themen regul{\"a}re Triangulierungen, Sekund{\"a}rpolytope, bistellare Operationen, h{\"o}here Stasheff-Tamari-Halbordnungen und Triangulierungen mit wenigen bzw. gar keinen Flips behandelt. Ein Kapitel {\"u}ber Enumeration und Optimierung beschließt die Zusammenstellung.}, language = {de} }