On the generalized lower bound conjecture for polytopes and spheres

• 成果类型: Article
• 署名作者: Murai, Satoshi; Nevo, Eran
• 署名单位: Yamaguchi University; Ben-Gurion University of the Negev
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0093-y
• 发表日期: 2013
• 页码: 185-202
• 关键词: convex; number; faces; PROOF

摘要

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), aEuro broken vertical bar, h (d) ) satisfies . Moreover, if h (r-1) = h (r) for some then P can be triangulated without introducing simplices of dimension a parts per thousand currency signd - 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 proof of the remaining part of the conjecture. In addition, we generalize this result to a certain class of simplicial spheres, namely those admitting the weak Lefschetz property.