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 $Vsubset M^d$ 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 $Vsubset M^d$ with $|V|=a$ is lexsegment (up to the permutations of the variables). In addition, we classify all Gotzmann subsets of $K[x_1,x_2,x_3]$.
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机译：多项式环的Gotzmann单项式理想是单次生成的理想式，它满足Gotzmann的持久性定理。令$ R = K [x_1， dots，x_n] $表示字段$ K $和$ M ^ d $上度为$ d $的$ R $的单项式的集合中$ n $变量的多项式环。如果$ V $生成的理想是Gotzmann单项式理想，则子集$ V 子集M ^ d $被称为Gotzmann子集。在本文中，我们找到所有整数$ a> 0 $，使得每个带有$ | V | = a $的Gotzmann子集$ V 子集M ^ d $是词段（直至变量的排列）。此外，我们对$ K [x_1，x_2，x_3] $的所有Gotzmann子集进行分类。
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