On the generalized lower bound conjecture for polytopes and spheres

Satoshi Murai, Eran Nevo

研究成果: Article査読

26 被引用数 (Scopus)

抄録

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, Moreover, if hr-1 = hr for some, 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 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.

本文言語English
ページ(範囲)185-202
ページ数18
ジャーナルActa Mathematica
210
1
DOI
出版ステータスPublished - 2013
外部発表はい

ASJC Scopus subject areas

  • Mathematics(all)

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