GOTZMANN MONOMIAL IDEALS

摘要

A Gotzmann monomial ideal of a polynomial ring is a monomial ideal which is generated in one degree and which satisfies Gotz-mann'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 is contained in 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 α ＞ 0 such that every Gotzmann subset V is contained in M~d with |V| = α is lexsegment (up to the permutations of the variables). In addition, we classify all Gotzmann subsets of K[x_1,X_2,X_3].