### Abstract

Let A = K[x _{1},..., x _{n}] denote the polynomial ring in n variables over a field K. We will classify all the Gotzmann ideals of A with at most n generators. In addition, we will study Hilbert functions H for which all homogeneous ideals of A with the Hilbert function H have the same graded Betti numbers. These Hilbert functions will be called inflexible Hilbert functions. We introduce the notion of segmentwise critical Hilbert functions and show that segmentwise critical Hilbert functions are inflexible.

Original language | English |
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Pages (from-to) | 629-646 |

Number of pages | 18 |

Journal | Mathematische Zeitschrift |

Volume | 260 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 Nov 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Murai, S., & Hibi, T. (2008). Gotzmann ideals of the polynomial ring.

*Mathematische Zeitschrift*,*260*(3), 629-646. https://doi.org/10.1007/s00209-007-0293-2