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# 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} }

- Published 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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