## Abstract

We prove that for d ≥ 3, the 1-skeleton of any (d-1)-dimensional doubly Cohen-Macaulay (abbreviated 2-CM) complex is generically d-rigid. This implies that Barnette's lower bound inequalities for boundary complexes of simplicial polytopes (Barnette, D. Isr. J. Math. 10:121-125, 1971; Barnette, D. Pac. J. Math. 46:349-354, 1973) hold for every 2-CM complex of dimension ≥ 2 (see Kalai, G. Invent. Math. 88:125-151, 1987). Moreover, the initial part (g _{0},g _{1},g _{2}) of the g-vector of a 2-CM complex (of dimension ≥ 3) is an M-sequence. It was conjectured by Björner and Swartz (J. Comb. Theory Ser. A 113:1305-1320, 2006) that the entire g-vector of a 2-CM complex is an M-sequence.

Original language | English |
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Pages (from-to) | 411-418 |

Number of pages | 8 |

Journal | Discrete and Computational Geometry |

Volume | 39 |

Issue number | 1-3 |

DOIs | |

State | Published - 1 Jan 2008 |

Externally published | Yes |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics