### Abstract

Given the f-vector f = (f _{0}, f _{1}, . . .) of a Cohen-Macaulay simplicial complex, it will be proved that there exists a shellable simplicial complex Δ _{f} with f(Δ _{f} ) = f such that, for any Cohen-Macaulay simplicial complex Δ with f(Δ) = f, one has β_{i}(Δ ≤ β_{i} I _{Δ}_ for all i and j, where f(Δ) is the f-vector of Δ and where β _{ij} (I _{Δ}) are graded Betti numbers of the Stanley-Reisner ideal I _{Δ} of Δ.

Original language | English |
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Pages (from-to) | 507-512 |

Number of pages | 6 |

Journal | Archiv der Mathematik |

Volume | 88 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2007 Jun 1 |

Externally published | Yes |

### Keywords

- Cohen-Macaulay simplicial complex
- F-vector
- Graded Betti number
- H-vector

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Murai, S., & Hibi, T. (2007). Maximal Betti numbers of Cohen-Macaulay complexes with a given f-vector.

*Archiv der Mathematik*,*88*(6), 507-512. https://doi.org/10.1007/s00013-007-1880-5