TY - GEN A1 - Lutz, Frank H. T1 - Triangulated Manifolds with Few Vertices: Combinatorial Manifolds N2 - 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. T3 - ZIB-Report - 06-08 KW - triangulated manifolds KW - combinatorial properties KW - minimal triangulations Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9028 ER - TY - GEN A1 - Lutz, Frank H. T1 - Small Examples of Non-Constructible Simplicial Balls and Spheres N2 - We construct non-constructible simplicial $d$-spheres with $d+10$ vertices and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices for $d\geq 3$. T3 - ZIB-Report - 03-28 KW - simplicial balls and spheres KW - constructibility KW - shellability KW - vertex-decomposability KW - knots in 3-balls and 3-spheres Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7500 ER - TY - GEN A1 - Lutz, Frank H. T1 - Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres N2 - 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. T3 - ZIB-Report - 04-11 KW - centrally symmetric polytopes KW - crosspolytope KW - combinatorial manifolds KW - products of spheres Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7863 ER - TY - GEN A1 - Rambau, Jörg T1 - Triangulierungen von Punktmengen und Polyedern N2 - Dieser Report wurde im Sommersemester 2000 an der TU Berlin in einer Spezialvorlesung über 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 weiterführende Themen reguläre Triangulierungen, Sekundärpolytope, bistellare Operationen, höhere Stasheff-Tamari-Halbordnungen und Triangulierungen mit wenigen bzw. gar keinen Flips behandelt. Ein Kapitel über Enumeration und Optimierung beschließt die Zusammenstellung. T3 - ZIB-Report - 00-46 KW - point configuration KW - triangulation KW - polytope KW - polyhedron KW - Gale diagram KW - secondary polytope KW - cyclic polytope KW - graph of all triangulations KW - conn Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6145 ER -