Remarks on missing faces and generalized lower bounds on face numbers
Abstract
Description
We consider simplicial polytopes, and more general simplicial complexes, without missing faces above a fixed dimension. Sharp analogues of McMullen's generalized lower bounds, and of Barnette's lower bounds, are conjectured for these families of complexes. Some partial results on these conjectures are presented.
11 pages. New content added: Conjecture 1.5 interpolates between the generalized lower bound conjecture for simplicial spheres and Gal's conjecture for flag spheres. To appear in Björner Festschrift, Elec. J. Combi.
11 pages. New content added: Conjecture 1.5 interpolates between the generalized lower bound conjecture for simplicial spheres and Gal's conjecture for flag spheres. To appear in Björner Festschrift, Elec. J. Combi.