Work

Lower Bound Theorems and a Generalized Lower Bound Conjecture for Balanced Simplicial Complexes

Year: 2016

Type: article

Abstract: A -dimensional simplicial complex is called balanced if its underlying graph admits a proper -coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs). Specifically, we prove the balanced analog of the celebrated lower bound theorem (LBT) for normal pseudomanifolds and characterize the case of equality; we introduce and characterize the balanced analog of the Walkup class; and we propose the balanced analog of the generalized lower bound conjecture (GLBC) and establish some related results. We close with constructions of balanced manifolds with few vertices.

Source: Mathematika

DOI: 10.1112/s0025579315000297

Authors: Steven Klee, Isabella Novik

Institutions: Seattle University, University of Washington

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Around the theory of f-vectors, Combinatorics, algebra, and geometry of face numbers