### Abstract

A Gotzmann monomial ideal of a polynomial ring is a monomial ideal which is generated in one degree and which satisfies Gotzmann's persistence theorem. Let R = K[x_{1},...,x_{n}] denote the polynomial ring in n variables over a field K and M^{d} the set of monomials of R of degree d. A subset V ⊂ M^{d} is said to be a Gotzmann subset if the ideal generated by V is a Gotzmann monomial ideal. In the present paper, we find all integers a > 0 such that every Gotzmann subset V ⊂ M^{d} with |V| = a is lexsegment (up to the permutations of the variables). In addition, we classify all Gotzmann subsets of K[x_{1}, x_{2}, x_{3}].

Original language | English |
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Pages (from-to) | 843-852 |

Number of pages | 10 |

Journal | Illinois Journal of Mathematics |

Volume | 51 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Jan 1 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Murai, S. (2007). Gotzmann monomial ideals.

*Illinois Journal of Mathematics*,*51*(3), 843-852. https://doi.org/10.1215/ijm/1258131105