### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Archiv der Mathematik*,

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

**Maximal Betti numbers of Cohen-Macaulay complexes with a given f-vector.** / Murai, Satoshi; Hibi, Takayuki.

Research output: Contribution to journal › Article

*Archiv der Mathematik*, vol. 88, no. 6, pp. 507-512. https://doi.org/10.1007/s00013-007-1880-5

}

TY - JOUR

T1 - Maximal Betti numbers of Cohen-Macaulay complexes with a given f-vector

AU - Murai, Satoshi

AU - Hibi, Takayuki

PY - 2007/6/1

Y1 - 2007/6/1

N2 - 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 βi(Δ ≤ βi 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.

AB - 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 βi(Δ ≤ βi 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.

KW - Cohen-Macaulay simplicial complex

KW - F-vector

KW - Graded Betti number

KW - H-vector

UR - http://www.scopus.com/inward/record.url?scp=34347264154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34347264154&partnerID=8YFLogxK

U2 - 10.1007/s00013-007-1880-5

DO - 10.1007/s00013-007-1880-5

M3 - Article

AN - SCOPUS:34347264154

VL - 88

SP - 507

EP - 512

JO - Archiv der Mathematik

JF - Archiv der Mathematik

SN - 0003-889X

IS - 6

ER -