### Abstract

Let A = K[x_{1}, . . ., x_{n}] denote the polynomial ring in n variables over a field K of characteristic 0 with each deg x_{i} = 1. Given arbitrary integers i and j with 2 ≤ i ≤ n and 3 ≤ j ≤ n, we will construct a monomial ideal I ⊂ A such that (i) β_{k}(I) < β_{k}(Gin(I)) for all k < i, (ii) β_{i}(I) = β_{i}(Gin(I)), (iii) β_{ℓ}(Gin(I)) < β_{ℓ}(Lex(I)) for all ℓ < j and (iv) β_{j}(Gin(I))=β_{j}(Lex(I)), where Gin(I) is the generic initial ideal of I with respect to the reverse lexicographic order induced by x_{1} > . . . > x_{n} and where Lex(I) is the lexsegment ideal with the same Hilbert function as I.

Original language | English |
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Pages (from-to) | 76-86 |

Number of pages | 11 |

Journal | Mathematica Scandinavica |

Volume | 99 |

Issue number | 1 |

Publication status | Published - 2006 Dec 11 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Murai, S., & Hibi, T. (2006). Gin and lex of certain monomial ideals.

*Mathematica Scandinavica*,*99*(1), 76-86.