## Illinois Journal of Mathematics

### Gotzmann monomial ideals

Satoshi Murai

#### 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 $R=K[x_1,\dots,x_n]$ 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 $V\subset M^d$ 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 $V\subset M^d$ with $|V|=a$ is lexsegment (up to the permutations of the variables). In addition, we classify all Gotzmann subsets of $K[x_1,x_2,x_3]$.

#### Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 843-852.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258131105

Digital Object Identifier
doi:10.1215/ijm/1258131105

Mathematical Reviews number (MathSciNet)
MR2379725

Zentralblatt MATH identifier
1155.13012

Subjects
Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Secondary: 05D05: Extremal set theory

#### Citation

Murai, Satoshi. Gotzmann monomial ideals. Illinois J. Math. 51 (2007), no. 3, 843--852. doi:10.1215/ijm/1258131105. https://projecteuclid.org/euclid.ijm/1258131105