### Abstract

Let S = K[x1, ⋯,xn] denote the polynomial ring in n variables over a field K with each deg xi = 1. Let Δ be a simplicial complex on [n] = {1, ⋯,n} and I. Δ S its Stanley-Reisner ideal. We write.e for the exterior algebraic shifted complex of Δ and.c for a combinatorial shifted complex of. Let ßii+j (I.) = dimK Tori(K, I.)i+j denote the graded Betti numbers of I. In the present paper it will be proved that (i) βii%+j (I.e) = βii%+j (I.c) for all i and j, where the base field is infinite, and (ii) βii%+j (I.) = βii%+j (I.c) for all i and j, where the base field is arbitrary. Thus in particular one has βii%+j (I.) = βii%+j (I.lex) for all i and j, where.lex is the unique lexsegment simplicial complex with the same f-vector as Δ and where the base field is arbitrary.

Original language | English |
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Pages (from-to) | 1853-1865 |

Number of pages | 13 |

Journal | Transactions of the American Mathematical Society |

Volume | 361 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Apr 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

*Transactions of the American Mathematical Society*,

*361*(4), 1853-1865. https://doi.org/10.1090/S0002-9947-08-04707-7