# MathSciDoc: An Archive for Mathematician ∫

#### CombinatoricsArithmetic Geometry and Commutative Algebramathscidoc:1701.06001

Acta Mathematica, 210, (1), 185-202, 2012.4
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 ($h$_{0},$h$_{1}, …,$h$_{$d$}) satisfies $${h_0}\leq {h_1}\leq \ldots \leq {h_{{\left\lfloor {{d \left/ {2} \right.}} \right\rfloor }}}$$ . Moreover, if$h$_{$r$−1}=$h$_{$r$}for some $$r\leq \frac{1}{2}d$$ then$P$can be triangulated without introducing simplices of dimension ≤$d$−$r$.
@inproceedings{satoshi2012on,
title={On the generalized lower bound conjecture for polytopes and spheres},
author={Satoshi Murai, and Eran Nevo},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203400559845769},
booktitle={Acta Mathematica},
volume={210},
number={1},
pages={185-202},
year={2012},
}
Satoshi Murai, and Eran Nevo. On the generalized lower bound conjecture for polytopes and spheres. 2012. Vol. 210. In Acta Mathematica. pp.185-202. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203400559845769.