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

Published online by Cambridge University Press:  01 February 2016

Steven Klee
Affiliation:
Department of Mathematics, Seattle University, Seattle, WA 98122, U.S.A. email [email protected]
Isabella Novik
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98195-4350, U.S.A. email [email protected]
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Abstract

A $(d-1)$-dimensional simplicial complex is called balanced if its underlying graph admits a proper $d$-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.

Type
Research Article
Copyright
Copyright © University College London 2016 

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