English

Remarks on missing faces and generalized lower bounds on face numbers

Combinatorics 2009-04-24 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0810.5487,
  title  = {Remarks on missing faces and generalized lower bounds on face numbers},
  author = {Eran Nevo},
  journal= {arXiv preprint arXiv:0810.5487},
  year   = {2009}
}

Comments

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 Bj\"orner Festschrift, Elec. J. Combi.

R2 v1 2026-06-21T11:36:35.116Z