LOWER BOUND THEOREMS AND A GENERALIZED LOWER BOUND CONJECTURE FOR BALANCED SIMPLICIAL COMPLEXES

DOI10.1112/S0025579315000297zbMath1337.05119arXiv1409.5094OpenAlexW3098716176WikidataQ123019664 ScholiaQ123019664MaRDI QIDQ2810734

Steven Klee, Isabella Novik

Publication date: 6 June 2016

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5094

zbMATH Keywords

lower bound theorem for normal pseudomanifolds

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Triangulating manifolds (57Q15) Coloring of graphs and hypergraphs (05C15) Polyhedral manifolds (52B70) Combinatorial aspects of simplicial complexes (05E45)

Related Items

Colorful versions of the Lebesgue, KKM, and Hex theorem ⋮ A generalized lower bound theorem for balanced manifolds ⋮ Octahedralizing \(3\)-colorable \(3\)-polytopes ⋮ Toric chordality ⋮ Graded Betti numbers of balanced simplicial complexes ⋮ Simplicial moves on balanced complexes ⋮ The existence of balanced neighborly polynomials ⋮ Balanced shellings and moves on balanced manifolds ⋮ A lower bound theorem for centrally symmetric simplicial polytopes ⋮ Balanced generalized lower bound inequality for simplicial polytopes ⋮ The rigidity of the graphs of homology spheres minus one edge ⋮ Minimal flag triangulations of lower-dimensional manifolds ⋮ Ear decomposition and balanced neighborly simplicial manifolds ⋮ Centrally symmetric and balanced triangulations of \(\mathbb{S}^2 \times \mathbb{S}^{d - 3}\) with few vertices ⋮ Minimal Balanced Triangulations of Sphere Bundles over the Circle ⋮ Balanced triangulations on few vertices and an implementation of cross-flips ⋮ Balanced triangulations on few vertices and an implementation of cross-flips ⋮ Triangulations of the product of spheres with few vertices

Cites Work

• On the generalized lower bound conjecture for polytopes and spheres
• On \(k\)-stellated and \(k\)-stacked spheres
• The mu vector, Morse inequalities and a generalized lower bound theorem for locally tame combinatorial manifolds
• Rigidity and the lower bound theorem. I
• Lower bounds for Buchsbaum\(^*\) complexes
• Balanced complexes and complexes without large missing faces
• Projectivities in simplicial complexes and colorings of simple polytopes
• Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets
• Higherdimensional analogues of Császár's torus
• \(g\)-elements, finite buildings and higher Cohen-Macaulay connectivity.
• Minimal triangulations of sphere bundles over the circle
• Topological finiteness for edge-vertex enumeration
• Lower bound theorem for normal pseudomanifolds
• Face enumeration-from spheres to manifolds
• Socles of Buchsbaum modules, complexes and posets
• Topological results in combinatorics
• The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem
• The number of faces of a simplicial convex polytope
• The rigidity of graphs. II
• A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
• Decompositions of homology manifolds and their graphs
• Flag \(f\)-vectors and the \(cd\)-index
• Lower-bound theorems for pseudomanifolds
• Combinatorics and commutative algebra.
• On \(r\)-stacked triangulated manifolds
• Graph theorems for manifolds
• Enumerative properties of triangulations of spherical bundles over \(S^1\)
• Decomposition theorem for the cd-index of Gorenstein posets
• The lower bound conjecture for 3- and 4-manifolds
• A proof of the lower bound conjecture for convex polytopes
• The classification of sphere bundles
• Shadows of colored complexes.
• A Combinatorial Analogue of Poincaré's Duality Theorem
• The cd-index of fans and posets
• A generalized lower‐bound conjecture for simplicial polytopes