On the Generalized Lower Bound Conjecture for Polytopes and Spheres

@inproceedings{Murai2012OnTG,
  title={On the Generalized Lower Bound Conjecture for Polytopes and Spheres},
  author={Satoshi Murai and Eran Nevo},
  year={2012}
}
In 1971, McMullen and Walkup posed the following conjecture, which is called the generalized lower bound conjecture: If P is a simplicial d-polytope then its h-vector (h0, h1, . . . , hd) satisfies h0 ≤ h1 ≤ · · · ≤ h⌊ d 2 ⌋. Moreover, if hr−1 = hr for some r ≤ d 2 then P can be triangulated without introducing simplices of dimension ≤ d− r. The first part of the conjecture was solved by Stanley in 1980 using the hard Lefschetz theorem for projective toric varieties. In this paper, we give a… CONTINUE READING
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